Rizzi, Peter; Sander, Evelyn; Wanner, Thomas Cyclic symmetry induced pitchfork bifurcations in the diblock copolymer model. (English) Zbl 07789742 Discrete Contin. Dyn. Syst., Ser. B 29, No. 2, 666-701 (2024). MSC: 37G40 37M20 65G20 65P30 37C81 65G30 74G60 74N15 PDFBibTeX XMLCite \textit{P. Rizzi} et al., Discrete Contin. Dyn. Syst., Ser. B 29, No. 2, 666--701 (2024; Zbl 07789742) Full Text: DOI arXiv
Nitta, Koki; Yamamoto, Nobito Numerical verification method on complex ODEs for existence of global solutions within finite domains. (English) Zbl 07780413 JSIAM Lett. 15, 69-72 (2023). MSC: 65P10 37J06 PDFBibTeX XMLCite \textit{K. Nitta} and \textit{N. Yamamoto}, JSIAM Lett. 15, 69--72 (2023; Zbl 07780413) Full Text: DOI
Balun, Jiří; Masopust, Tomáš Verifying weak and strong \(k\)-step opacity in discrete-event systems. (English) Zbl 1520.93305 Automatica 155, Article ID 111153, 12 p. (2023). MSC: 93C65 93B07 37B15 PDFBibTeX XMLCite \textit{J. Balun} and \textit{T. Masopust}, Automatica 155, Article ID 111153, 12 p. (2023; Zbl 1520.93305) Full Text: DOI arXiv
Baldomá, Inmaculada; Capiński, Maciej J.; Guardia, Marcel; Seara, Tere M. Breakdown of heteroclinic connections in the analytic Hopf-zero singularity: rigorous computation of the Stokes constant. (English) Zbl 1510.37079 J. Nonlinear Sci. 33, No. 2, Paper No. 28, 47 p. (2023). MSC: 37G10 37G20 34C23 37C75 37M20 37M21 37D10 65G20 PDFBibTeX XMLCite \textit{I. Baldomá} et al., J. Nonlinear Sci. 33, No. 2, Paper No. 28, 47 p. (2023; Zbl 1510.37079) Full Text: DOI arXiv
Constantineau, Kevin; García-Azpeitia, Carlos; García-Naranjo, Luis C; Lessard, Jean-Philippe Determination of stable branches of relative equilibria of the \(N\)-vortex problem on the sphere. arXiv:2309.04320 Preprint, arXiv:2309.04320 [math.DS] (2023). MSC: 70K42 76M60 65G30 65G20 47H10 37C25 BibTeX Cite \textit{K. Constantineau} et al., ``Determination of stable branches of relative equilibria of the $N$-vortex problem on the sphere'', Preprint, arXiv:2309.04320 [math.DS] (2023) Full Text: arXiv OA License
Karimov, Toghrul; Kelmendi, Edon; Ouaknine, Joël; Worrell, James What’s decidable about discrete linear dynamical systems? (English) Zbl 1528.68228 Raskin, Jean-François (ed.) et al., Principles of systems design. Essays dedicated to Thomas A. Henzinger on the occasion of his 60th birthday. Cham: Springer. Lect. Notes Comput. Sci. 13660, 21-38 (2022). MSC: 68Q60 03B25 11B37 37B10 93B03 PDFBibTeX XMLCite \textit{T. Karimov} et al., Lect. Notes Comput. Sci. 13660, 21--38 (2022; Zbl 1528.68228) Full Text: DOI arXiv
Kamimoto, Sayomi; Kim, Hye Kyung; Sander, Evelyn; Wanner, Thomas A computer-assisted study of red coral population dynamics. (English) Zbl 1506.37109 Pure Appl. Funct. Anal. 7, No. 4, 1307-1337 (2022). MSC: 37M20 65G20 65P30 65G30 92D25 92D40 PDFBibTeX XMLCite \textit{S. Kamimoto} et al., Pure Appl. Funct. Anal. 7, No. 4, 1307--1337 (2022; Zbl 1506.37109) Full Text: arXiv Link
Kapela, Tomasz; Wilczak, Daniel; Zgliczyński, Piotr Recent advances in a rigorous computation of Poincaré maps. (English) Zbl 1503.37088 Commun. Nonlinear Sci. Numer. Simul. 110, Article ID 106366, 22 p. (2022). Reviewer: Fernando Casas (Castellon) MSC: 37M99 37C27 65G20 PDFBibTeX XMLCite \textit{T. Kapela} et al., Commun. Nonlinear Sci. Numer. Simul. 110, Article ID 106366, 22 p. (2022; Zbl 1503.37088) Full Text: DOI arXiv
Nitta, Koki; Yamamoto, Nobito; Matsue, Kaname A numerical verification method to specify homoclinic orbits as application of local Lyapunov functions. (English) Zbl 1505.34068 Japan J. Ind. Appl. Math. 39, No. 2, 467-513 (2022). Reviewer: Cristian Vladimirescu (Craiova) MSC: 34C37 34D20 37M21 65G30 PDFBibTeX XMLCite \textit{K. Nitta} et al., Japan J. Ind. Appl. Math. 39, No. 2, 467--513 (2022; Zbl 1505.34068) Full Text: DOI
Beck, Margaret; Jaquette, Jonathan Validated spectral stability via conjugate points. (English) Zbl 1494.37046 SIAM J. Appl. Dyn. Syst. 21, No. 1, 366-404 (2022). Reviewer: Svetlin Georgiev (Sofia) MSC: 37L15 35K57 35B35 34B24 37M20 37M21 65G20 PDFBibTeX XMLCite \textit{M. Beck} and \textit{J. Jaquette}, SIAM J. Appl. Dyn. Syst. 21, No. 1, 366--404 (2022; Zbl 1494.37046) Full Text: DOI arXiv
Capiński, Maciej J.; Krauskopf, Bernd; Osinga, Hinke M.; Zgliczyński, Piotr Characterising blenders via covering relations and cone conditions. arXiv:2212.04861 Preprint, arXiv:2212.04861 [math.DS] (2022). MSC: 37M21 37D30 65G20 37C29 37B20 BibTeX Cite \textit{M. J. Capiński} et al., ``Characterising blenders via covering relations and cone conditions'', Preprint, arXiv:2212.04861 [math.DS] (2022) Full Text: arXiv OA License
Burbanks, Andrew D.; Osbaldestin, Andrew H.; Thurlby, Judi A. Rigorous computer-assisted bounds on the period doubling renormalization fixed point and eigenfunctions in maps with critical point of degree 4. (English) Zbl 1486.37024 J. Math. Phys. 62, No. 11, Article ID 112701, 18 p. (2021). MSC: 37E20 37E25 65G20 65G30 PDFBibTeX XMLCite \textit{A. D. Burbanks} et al., J. Math. Phys. 62, No. 11, Article ID 112701, 18 p. (2021; Zbl 1486.37024) Full Text: DOI arXiv
Li, Zhijun; Fang, Siyuan; Ma, Minglin; Wang, Mengjiao Bursting oscillations and experimental verification of a Rucklidge system. (English) Zbl 1473.37061 Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 8, Article ID 2130023, 13 p. (2021). MSC: 37G10 37G15 37M20 34N05 PDFBibTeX XMLCite \textit{Z. Li} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 8, Article ID 2130023, 13 p. (2021; Zbl 1473.37061) Full Text: DOI
Sander, Evelyn; Wanner, Thomas Equilibrium validation in models for pattern formation based on Sobolev embeddings. (English) Zbl 1465.35050 Discrete Contin. Dyn. Syst., Ser. B 26, No. 1, 603-632 (2021). MSC: 35B36 35B32 35B40 35B41 35K35 35K58 37M20 65G20 65G30 65N35 PDFBibTeX XMLCite \textit{E. Sander} and \textit{T. Wanner}, Discrete Contin. Dyn. Syst., Ser. B 26, No. 1, 603--632 (2021; Zbl 1465.35050) Full Text: DOI arXiv
Calleja, Renato; García-Azpeitia, Carlos; Lessard, Jean-Philippe; Mireles James, J. D. Torus knot choreographies in the \(n\)-body problem. (English) Zbl 1476.70035 Nonlinearity 34, No. 1, 313-348 (2021). MSC: 70F10 70F15 34K13 37C27 37J46 47H10 65G20 PDFBibTeX XMLCite \textit{R. Calleja} et al., Nonlinearity 34, No. 1, 313--348 (2021; Zbl 1476.70035) Full Text: DOI arXiv
Becchi, Anna; Cimatti, Alessandro; Zaffanella, Enea Synthesis of P-stable abstractions. (English) Zbl 1476.68059 de Boer, Frank (ed.) et al., Software engineering and formal methods. 18th international conference, SEFM 2020, Amsterdam, The Netherlands, September 14–18, 2020. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12310, 214-230 (2020). MSC: 68N30 37B25 PDFBibTeX XMLCite \textit{A. Becchi} et al., Lect. Notes Comput. Sci. 12310, 214--230 (2020; Zbl 1476.68059) Full Text: DOI
Sankaranarayanan, Sriram Reachability analysis using message passing over tree decompositions. (English) Zbl 1478.68173 Lahiri, Shuvendu Kumar (ed.) et al., Computer aided verification. 32nd international conference, CAV 2020, Los Angeles, CA, USA, July 21–24, 2020. Proceedings. Part I. Cham: Springer. Lect. Notes Comput. Sci. 12224, 604-628 (2020). MSC: 68Q60 37B10 68R10 93B03 PDFBibTeX XMLCite \textit{S. Sankaranarayanan}, Lect. Notes Comput. Sci. 12224, 604--628 (2020; Zbl 1478.68173) Full Text: DOI
Capiński, Maciej J.; Fleurantin, Emmanuel; Mireles James, J. D. Computer assisted proofs of two-dimensional attracting invariant tori for ODEs. (English) Zbl 1459.37079 Discrete Contin. Dyn. Syst. 40, No. 12, 6681-6707 (2020). Reviewer: Mohammad Sajid (Buraidah) MSC: 37M22 37M21 37M20 37C10 34C45 37G35 65P20 65G20 68V05 PDFBibTeX XMLCite \textit{M. J. Capiński} et al., Discrete Contin. Dyn. Syst. 40, No. 12, 6681--6707 (2020; Zbl 1459.37079) Full Text: DOI arXiv
Lessard, J. P.; Mireles James, J. D. A functional analytic approach to validated numerics for eigenvalues of delay equations. (English) Zbl 07235863 J. Comput. Dyn. 7, No. 1, 123-158 (2020). MSC: 65G20 37B30 34K08 34K20 65M70 PDFBibTeX XMLCite \textit{J. P. Lessard} and \textit{J. D. Mireles James}, J. Comput. Dyn. 7, No. 1, 123--158 (2020; Zbl 07235863) Full Text: DOI
Walawska, Irmina; Wilczak, Daniel Validated numerics for period-tupling and touch-and-go bifurcations of symmetric periodic orbits in reversible systems. (English) Zbl 1464.65282 Commun. Nonlinear Sci. Numer. Simul. 74, 30-54 (2019). MSC: 65P30 65G20 37M20 37C27 70F07 70M20 PDFBibTeX XMLCite \textit{I. Walawska} and \textit{D. Wilczak}, Commun. Nonlinear Sci. Numer. Simul. 74, 30--54 (2019; Zbl 1464.65282) Full Text: DOI arXiv
Breden, Maxime; Kuehn, Christian Rigorous validation of stochastic transition paths. (English. French summary) Zbl 1427.60142 J. Math. Pures Appl. (9) 131, 88-129 (2019). Reviewer: Ivan Podvigin (Novosibirsk) MSC: 60H35 65G20 34C45 37C29 37J51 PDFBibTeX XMLCite \textit{M. Breden} and \textit{C. Kuehn}, J. Math. Pures Appl. (9) 131, 88--129 (2019; Zbl 1427.60142) Full Text: DOI arXiv
Fijalkow, Nathanaël; Ohlmann, Pierre; Ouaknine, Joël; Pouly, Amaury; Worrell, James Complete semialgebraic invariant synthesis for the Kannan-Lipton orbit problem. (English) Zbl 1461.37028 Theory Comput. Syst. 63, No. 5, 1027-1048 (2019). MSC: 37C35 37C79 68U05 PDFBibTeX XMLCite \textit{N. Fijalkow} et al., Theory Comput. Syst. 63, No. 5, 1027--1048 (2019; Zbl 1461.37028) Full Text: DOI arXiv HAL
Nepomuceno, Erivelton G.; Martins, Samir A. M.; Silva, Bruno C.; Amaral, Gleison F. V.; Perc, Matjaž Detecting unreliable computer simulations of recursive functions with interval extensions. (English) Zbl 1427.65411 Appl. Math. Comput. 329, 408-419 (2018). MSC: 65Q20 37D45 65G20 PDFBibTeX XMLCite \textit{E. G. Nepomuceno} et al., Appl. Math. Comput. 329, 408--419 (2018; Zbl 1427.65411) Full Text: DOI
Mischaikow, Konstantin Rigorous computational dynamics in the context of unknown nonlinearities. (English) Zbl 1404.37112 van den Berg, Jan Bouwe (ed.) et al., Rigorous numerics in dynamics. AMS short course, Seattle, WA, USA, January 4–5, 2016. Lecture notes. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2814-3/hbk; 978-1-4704-4729-8/ebook). Proceedings of Symposia in Applied Mathematics 74, 195-213 (2018). MSC: 37N25 37M99 65G20 92C42 PDFBibTeX XMLCite \textit{K. Mischaikow}, Proc. Symp. Appl. Math. 74, 195--213 (2018; Zbl 1404.37112) Full Text: DOI
James, J. D. Mireles Validated numerics for equilibria of analytic vector fields: invariant manifolds and connecting orbits. (English) Zbl 1409.65109 van den Berg, Jan Bouwe (ed.) et al., Rigorous numerics in dynamics. AMS short course, Seattle, WA, USA, January 4–5, 2016. Lecture notes. Providence, RI: American Mathematical Society (AMS). Proc. Symp. Appl. Math. 74, 27-80 (2018). Reviewer: Stathis Antoniou (Athína) MSC: 65P30 34C45 34C37 65G20 37M25 PDFBibTeX XMLCite \textit{J. D. M. James}, Proc. Symp. Appl. Math. 74, 27--80 (2018; Zbl 1409.65109) Full Text: DOI
Capiński, Maciej J.; Zgliczyński, Piotr Beyond the Melnikov method. II: Multidimensional setting. (English) Zbl 1400.37031 J. Differ. Equations 265, No. 9, 3988-4015 (2018). MSC: 37D10 37C29 65G20 PDFBibTeX XMLCite \textit{M. J. Capiński} and \textit{P. Zgliczyński}, J. Differ. Equations 265, No. 9, 3988--4015 (2018; Zbl 1400.37031) Full Text: DOI arXiv
Breden, Maxime; Lessard, Jean-Philippe Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs. (English) Zbl 1398.65092 Discrete Contin. Dyn. Syst., Ser. B 23, No. 7, 2825-2858 (2018). MSC: 65G20 65P99 65D30 37M99 37C27 PDFBibTeX XMLCite \textit{M. Breden} and \textit{J.-P. Lessard}, Discrete Contin. Dyn. Syst., Ser. B 23, No. 7, 2825--2858 (2018; Zbl 1398.65092) Full Text: DOI arXiv
Immler, Fabian A verified ODE solver and the Lorenz attractor. (English) Zbl 1448.68460 J. Autom. Reasoning 61, No. 1-4, 73-111 (2018). MSC: 68V15 34-04 34A34 37D45 65G20 65L05 PDFBibTeX XMLCite \textit{F. Immler}, J. Autom. Reasoning 61, No. 1--4, 73--111 (2018; Zbl 1448.68460) Full Text: DOI
Omidvar, Hamed; Franceschetti, Massimo Self-organized segregation on the grid. (English) Zbl 1391.82015 J. Stat. Phys. 170, No. 4, 748-783 (2018). MSC: 82B20 82B43 68Q60 37B15 PDFBibTeX XMLCite \textit{H. Omidvar} and \textit{M. Franceschetti}, J. Stat. Phys. 170, No. 4, 748--783 (2018; Zbl 1391.82015) Full Text: DOI arXiv
Schivo, Stefano; Langerak, Rom Discretization of continuous dynamical systems using UPPAAL. (English) Zbl 1498.68142 Katoen, Joost-Pieter (ed.) et al., ModelEd, testEd, trustEd. Essays dedicated to Ed Brinksma on the occasion of his 60th birthday. Cham: Springer. Lect. Notes Comput. Sci. 10500, 297-315 (2017). MSC: 68Q45 37M15 65L05 68Q60 92C42 PDFBibTeX XMLCite \textit{S. Schivo} and \textit{R. Langerak}, Lect. Notes Comput. Sci. 10500, 297--315 (2017; Zbl 1498.68142) Full Text: DOI
Fijalkow, Nathanaël; Ohlmann, Pierre; Ouaknine, Joël; Pouly, Amaury; Worrell, James Semialgebraic invariant synthesis for the Kannan-Lipton orbit problem. (English) Zbl 1434.37008 Vollmer, Heribert (ed.) et al., 34th symposium on theoretical aspects of computer science (STACS 2017), Hannover, Germany, March 8–11, 2017. Proceedings. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 66, Article 29, 13 p. (2017). MSC: 37B20 03B25 15A72 37C35 PDFBibTeX XMLCite \textit{N. Fijalkow} et al., LIPIcs -- Leibniz Int. Proc. Inform. 66, Article 29, 13 p. (2017; Zbl 1434.37008) Full Text: DOI
Figueras, J.-Ll.; Haro, A.; Luque, A. Rigorous computer-assisted application of KAM theory: a modern approach. (English) Zbl 1383.37047 Found. Comput. Math. 17, No. 5, 1123-1193 (2017). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 37J40 37J10 65G20 65G40 65T50 PDFBibTeX XMLCite \textit{J. Ll. Figueras} et al., Found. Comput. Math. 17, No. 5, 1123--1193 (2017; Zbl 1383.37047) Full Text: DOI arXiv
Ratschan, Stefan Simulation based computation of certificates for safety of dynamical systems. (English) Zbl 1494.68172 Abate, Alessandro (ed.) et al., Formal modeling and analysis of timed systems. 15th international conference, FORMATS 2017, Berlin, Germany, September 5–7, 2017. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 10419, 303-317 (2017). MSC: 68Q60 37M05 PDFBibTeX XMLCite \textit{S. Ratschan}, Lect. Notes Comput. Sci. 10419, 303--317 (2017; Zbl 1494.68172) Full Text: DOI arXiv
Salo, Ville Decidability and universality of quasiminimal subshifts. (English) Zbl 1372.68103 J. Comput. Syst. Sci. 89, 288-314 (2017). MSC: 68Q05 37B10 37B50 68Q45 68Q60 PDFBibTeX XMLCite \textit{V. Salo}, J. Comput. Syst. Sci. 89, 288--314 (2017; Zbl 1372.68103) Full Text: DOI arXiv
Capiński, Maciej J.; Wasieczko-Zając, Anna Computer-assisted proof of Shil’nikov homoclinics: with application to the Lorenz-84 model. (English) Zbl 1371.34061 SIAM J. Appl. Dyn. Syst. 16, No. 3, 1453-1473 (2017). MSC: 34C37 37D05 37D10 65G20 34C45 PDFBibTeX XMLCite \textit{M. J. Capiński} and \textit{A. Wasieczko-Zając}, SIAM J. Appl. Dyn. Syst. 16, No. 3, 1453--1473 (2017; Zbl 1371.34061) Full Text: DOI arXiv
Huang, Zhenqi; Fan, Chuchu; Mitra, Sayan Bounded invariant verification for time-delayed nonlinear networked dynamical systems. (English) Zbl 1353.37173 Nonlinear Anal., Hybrid Syst. 23, 211-229 (2017). MSC: 37N35 93C15 93C10 90B10 PDFBibTeX XMLCite \textit{Z. Huang} et al., Nonlinear Anal., Hybrid Syst. 23, 211--229 (2017; Zbl 1353.37173) Full Text: DOI
Capiński, Maciej J.; Zgliczyński, Piotr Beyond the Melnikov method: A computer assisted approach. (English) Zbl 1368.37035 J. Differ. Equations 262, No. 1, 365-417 (2017). MSC: 37D10 65G20 37M99 70H33 65P40 PDFBibTeX XMLCite \textit{M. J. Capiński} and \textit{P. Zgliczyński}, J. Differ. Equations 262, No. 1, 365--417 (2017; Zbl 1368.37035) Full Text: DOI arXiv
Yang, Zhengfeng; Huang, Chao; Chen, Xin; Lin, Wang; Liu, Zhiming A linear programming relaxation based approach for generating barrier certificates of hybrid systems. (English) Zbl 1427.68176 Fitzgerald, John (ed.) et al., FM 2016: formal methods. 21st international symposium, Limassol, Cyprus, November 9–11, 2016. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9995, 721-738 (2016). MSC: 68Q60 37B10 90C90 PDFBibTeX XMLCite \textit{Z. Yang} et al., Lect. Notes Comput. Sci. 9995, 721--738 (2016; Zbl 1427.68176) Full Text: DOI
Chen, Mingshuai; Fränzle, Martin; Li, Yangjia; Mosaad, Peter N.; Zhan, Naijun Validated simulation-based verification of delayed differential dynamics. (English) Zbl 1427.68163 Fitzgerald, John (ed.) et al., FM 2016: formal methods. 21st international symposium, Limassol, Cyprus, November 9–11, 2016. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9995, 137-154 (2016). MSC: 68Q60 34K05 37C10 PDFBibTeX XMLCite \textit{M. Chen} et al., Lect. Notes Comput. Sci. 9995, 137--154 (2016; Zbl 1427.68163) Full Text: DOI
Beneš, Nikola; Brim, Luboš; Demko, Martin; Pastva, Samuel; Šafránek, David A model checking approach to discrete bifurcation analysis. (English) Zbl 1427.68159 Fitzgerald, John (ed.) et al., FM 2016: formal methods. 21st international symposium, Limassol, Cyprus, November 9–11, 2016. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9995, 85-101 (2016). MSC: 68Q60 03B44 37G10 92C42 PDFBibTeX XMLCite \textit{N. Beneš} et al., Lect. Notes Comput. Sci. 9995, 85--101 (2016; Zbl 1427.68159) Full Text: DOI
Weilandt, Frank; Mrozek, Marian; Mischaikow, Konstantin Discretization strategies for computing Conley indices and Morse decompositions of flows. (English) Zbl 1373.37043 J. Comput. Dyn. 3, No. 1, 1-16 (2016). MSC: 37B30 37B35 65G20 65P40 PDFBibTeX XMLCite \textit{F. Weilandt} et al., J. Comput. Dyn. 3, No. 1, 1--16 (2016; Zbl 1373.37043) Full Text: DOI arXiv
de la Llave, R.; Mireles James, J. D. Connecting orbits for compact infinite dimensional maps: computer assisted proofs of existence. (English) Zbl 1343.37078 SIAM J. Appl. Dyn. Syst. 15, No. 2, 1268-1323 (2016). MSC: 37L25 37M99 65P99 65G20 PDFBibTeX XMLCite \textit{R. de la Llave} and \textit{J. D. Mireles James}, SIAM J. Appl. Dyn. Syst. 15, No. 2, 1268--1323 (2016; Zbl 1343.37078) Full Text: DOI
van der Hoeven, Joris Certifying trajectories of dynamical systems. (English) Zbl 1460.37078 Kotsireas, Ilias S. (ed.) et al., Mathematical aspects of computer and information sciences. 6th international conference, MACIS 2015, Berlin, Germany, November 11–13, 2015. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 9582, 520-532 (2016). MSC: 37M99 65L05 65G20 PDFBibTeX XMLCite \textit{J. van der Hoeven}, Lect. Notes Comput. Sci. 9582, 520--532 (2016; Zbl 1460.37078) Full Text: DOI HAL
Breden, Maxime; Lessard, Jean-Philippe; Mireles James, Jason D. Computation of maximal local (un)stable manifold patches by the parameterization method. (English) Zbl 1336.65197 Indag. Math., New Ser. 27, No. 1, 340-367 (2016). MSC: 65P40 34C45 34C37 37D10 37C29 37M99 65G20 70H33 PDFBibTeX XMLCite \textit{M. Breden} et al., Indag. Math., New Ser. 27, No. 1, 340--367 (2016; Zbl 1336.65197) Full Text: DOI arXiv
Birrell, Jeremiah A posteriori error bounds for two point boundary value problems: a Green’s function approach. (English) Zbl 1366.37050 J. Comput. Dyn. 2, No. 2, 143-164 (2015). MSC: 37C27 65G20 34B15 34B27 65L10 65L11 65L70 PDFBibTeX XMLCite \textit{J. Birrell}, J. Comput. Dyn. 2, No. 2, 143--164 (2015; Zbl 1366.37050) Full Text: DOI arXiv
Immler, Fabian A verified enclosure for the Lorenz attractor (rough diamond). (English) Zbl 1465.65040 Urban, Christian (ed.) et al., Interactive theorem proving. 6th international conference, ITP 2015, Nanjing, China, August 24–27, 2015. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 9236, 221-226 (2015). MSC: 65G20 34D45 37C10 37D45 68V15 PDFBibTeX XMLCite \textit{F. Immler}, Lect. Notes Comput. Sci. 9236, 221--226 (2015; Zbl 1465.65040) Full Text: DOI
Zgliczyński, Piotr Steady state bifurcations for the Kuramoto-Sivashinsky equation: a computer assisted proof. (English) Zbl 1326.35029 J. Comput. Dyn. 2, No. 1, 95-142 (2015). MSC: 35B32 37G10 65G20 PDFBibTeX XMLCite \textit{P. Zgliczyński}, J. Comput. Dyn. 2, No. 1, 95--142 (2015; Zbl 1326.35029) Full Text: DOI
Miyaji, Tomoyuki; Okamoto, Hisashi; Craik, Alex D. D. A four-leaf chaotic attractor of a three-dimensional dynamical system. (English) Zbl 1309.37040 Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 2, Article ID 1530003, 21 p. (2015). MSC: 37D45 37C70 37G15 34C28 34C23 37M20 PDFBibTeX XMLCite \textit{T. Miyaji} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 25, No. 2, Article ID 1530003, 21 p. (2015; Zbl 1309.37040) Full Text: DOI
Ghorbal, Khalil; Sogokon, Andrew; Platzer, André A hierarchy of proof rules for checking differential invariance of algebraic sets. (English) Zbl 1432.68262 D’Souza, Deepak (ed.) et al., Verification, model checking, and abstract interpretation. 16th international conference, VMCAI 2015, Mumbai, India, January 12–14, 2015. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8931, 431-448 (2015). MSC: 68Q60 37C10 PDFBibTeX XMLCite \textit{K. Ghorbal} et al., Lect. Notes Comput. Sci. 8931, 431--448 (2015; Zbl 1432.68262) Full Text: DOI HAL
Fullmer, William D.; Lopez de Bertodano, Martin A.; Chen, Min; Clausse, Alejandro Analysis of stability, verification and chaos with the Kreiss-Yström equations. (English) Zbl 1338.35361 Appl. Math. Comput. 248, 28-46 (2014). MSC: 35Q35 35B25 35K40 35R25 37N15 76Txx PDFBibTeX XMLCite \textit{W. D. Fullmer} et al., Appl. Math. Comput. 248, 28--46 (2014; Zbl 1338.35361) Full Text: DOI
Miyaji, Tomoyuki; Okamoto, Hisashi A computer-assisted proof of existence of a periodic solution. (English) Zbl 1348.37037 Proc. Japan Acad., Ser. A 90, No. 10, 139-144 (2014). MSC: 37C27 65G20 37M05 34C11 34C25 PDFBibTeX XMLCite \textit{T. Miyaji} and \textit{H. Okamoto}, Proc. Japan Acad., Ser. A 90, No. 10, 139--144 (2014; Zbl 1348.37037) Full Text: DOI Euclid
Szczelina, Robert; Zgliczyński, Piotr A homoclinic orbit in a planar singular ODE – a computer assisted proof. (English) Zbl 1284.34070 SIAM J. Appl. Dyn. Syst. 12, No. 3, 1541-1565 (2013). MSC: 34C37 37G20 65G20 34A09 PDFBibTeX XMLCite \textit{R. Szczelina} and \textit{P. Zgliczyński}, SIAM J. Appl. Dyn. Syst. 12, No. 3, 1541--1565 (2013; Zbl 1284.34070) Full Text: DOI Link
Mireles James, J. D.; Mischaikow, Konstantin Rigorous a posteriori computation of (un)stable manifolds and connecting orbits for analytic maps. (English) Zbl 1330.37029 SIAM J. Appl. Dyn. Syst. 12, No. 2, 957-1006 (2013). MSC: 37D10 37C29 65G20 65P20 PDFBibTeX XMLCite \textit{J. D. Mireles James} and \textit{K. Mischaikow}, SIAM J. Appl. Dyn. Syst. 12, No. 2, 957--1006 (2013; Zbl 1330.37029) Full Text: DOI
Bournez, Olivier; Graça, Daniel S.; Hainry, Emmanuel Computation with perturbed dynamical systems. (English) Zbl 1410.68119 J. Comput. Syst. Sci. 79, No. 5, 714-724 (2013). MSC: 68Q05 03D78 37N99 68Q45 68Q60 PDFBibTeX XMLCite \textit{O. Bournez} et al., J. Comput. Syst. Sci. 79, No. 5, 714--724 (2013; Zbl 1410.68119) Full Text: DOI
Dankowicz, Harry; Schilder, Frank Recipes for continuation. (English) Zbl 1277.65037 Computational Science & Engineering 11. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 978-1-611972-56-6/pbk; 978-1-61197-257-3/ebook). xv, 584 p. (2013). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 65H20 65-02 65Y20 68N30 34B15 65L10 65P30 37G15 PDFBibTeX XMLCite \textit{H. Dankowicz} and \textit{F. Schilder}, Recipes for continuation. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2013; Zbl 1277.65037) Full Text: DOI
Platzer, André Logics of dynamical systems. (English) Zbl 1362.68178 Proceedings of the 2012 27th annual ACM/IEEE symposium on logic in computer science, LICS 2012, Dubrovnik, Croatia, June 25–28, 2012. Los Alamitos, CA: IEEE Computer Society (ISBN 978-0-7695-4769-5). 13-24 (2012). MSC: 68Q60 03B45 03B70 37B10 93C95 PDFBibTeX XMLCite \textit{A. Platzer}, in: Proceedings of the 2012 27th annual ACM/IEEE symposium on logic in computer science, LICS 2012, Dubrovnik, Croatia, June 25--28, 2012. Los Alamitos, CA: IEEE Computer Society. 13--24 (2012; Zbl 1362.68178) Full Text: DOI
Carter, Rebekah; Navarro-López, Eva M. Dynamically-driven timed automaton abstractions for proving liveness of continuous systems. (English) Zbl 1375.68072 Jurdziński, Marcin (ed.) et al., Formal modeling and analysis of timed systems. 10th international conference, FORMATS 2012, London, UK, September 18-20, 2012. Proceedings. Berlin: Springer (ISBN 978-3-642-33364-4/pbk). Lecture Notes in Computer Science 7595, 59-74 (2012). MSC: 68Q45 37B10 PDFBibTeX XMLCite \textit{R. Carter} and \textit{E. M. Navarro-López}, Lect. Notes Comput. Sci. 7595, 59--74 (2012; Zbl 1375.68072) Full Text: DOI
Furia, Carlo A.; Mandrioli, Dino; Morzenti, Angelo; Rossi, Matteo Modeling time in computing. (English) Zbl 1260.68004 Monographs in Theoretical Computer Science. An EATCS Series. Berlin: Springer (ISBN 978-3-642-32331-7/hbk; 978-3-642-32332-4/ebook). xvi, 423 p. (2012). Reviewer: Florin Manea (Berlin) MSC: 68-02 68Q85 68Q05 68Q25 68W40 68Q60 37N99 PDFBibTeX XMLCite \textit{C. A. Furia} et al., Modeling time in computing. Berlin: Springer (2012; Zbl 1260.68004) Full Text: DOI
Capiński, Maciej J.; Simó, Carles Computer assisted proof for normally hyperbolic invariant manifolds. (English) Zbl 1256.37020 Nonlinearity 25, No. 7, 1997-2026 (2012). MSC: 37D10 37D25 37M05 37D45 PDFBibTeX XMLCite \textit{M. J. Capiński} and \textit{C. Simó}, Nonlinearity 25, No. 7, 1997--2026 (2012; Zbl 1256.37020) Full Text: DOI arXiv
Platzer, André Dynamic Logics of Dynamical Systems. arXiv:1205.4788 Preprint, arXiv:1205.4788 [cs.LO] (2012). MSC: 03B70 03B45 03F03 68Q60 34A38 68M14 34C45 37H10 60H10 03D78 BibTeX Cite \textit{A. Platzer}, ``Dynamic Logics of Dynamical Systems'', Preprint, arXiv:1205.4788 [cs.LO] (2012) Full Text: arXiv OA License
Johnson, Tomas A quartic system with twenty-six limit cycles. (English) Zbl 1267.34059 Exp. Math. 20, No. 3, 323-328 (2011). Reviewer: Douglas S. Shafer (Charlotte) MSC: 34C07 34C23 37G15 37M20 65G20 PDFBibTeX XMLCite \textit{T. Johnson}, Exp. Math. 20, No. 3, 323--328 (2011; Zbl 1267.34059) Full Text: DOI Euclid
Goldsztejn, Alexandre; Hayes, Wayne; Collins, Pieter Tinkerbell is chaotic. (English) Zbl 1235.37027 SIAM J. Appl. Dyn. Syst. 10, No. 4, 1480-1501 (2011). MSC: 37M99 65G20 65G30 37D45 PDFBibTeX XMLCite \textit{A. Goldsztejn} et al., SIAM J. Appl. Dyn. Syst. 10, No. 4, 1480--1501 (2011; Zbl 1235.37027) Full Text: DOI Link
Sloth, Christoffer; Wisniewski, Rafael Verification of continuous dynamical systems by timed automata. (English) Zbl 1233.68158 Form. Methods Syst. Des. 39, No. 1, 47-82 (2011). MSC: 68Q60 37C10 68Q45 37B25 PDFBibTeX XMLCite \textit{C. Sloth} and \textit{R. Wisniewski}, Form. Methods Syst. Des. 39, No. 1, 47--82 (2011; Zbl 1233.68158) Full Text: DOI Link
Ippei, Obayashi Computer-assisted verification method for invariant densities and rates of decay of correlations. (English) Zbl 1223.37007 SIAM J. Appl. Dyn. Syst. 10, No. 2, 788-816 (2011). MSC: 37A25 37M25 37E05 65G20 PDFBibTeX XMLCite \textit{O. Ippei}, SIAM J. Appl. Dyn. Syst. 10, No. 2, 788--816 (2011; Zbl 1223.37007) Full Text: DOI
Luzzatto, Stefano; Pilarczyk, Paweł Finite resolution dynamics. (English) Zbl 1211.65164 Found. Comput. Math. 11, No. 2, 211-239 (2011). MSC: 65P20 37M99 65G20 PDFBibTeX XMLCite \textit{S. Luzzatto} and \textit{P. Pilarczyk}, Found. Comput. Math. 11, No. 2, 211--239 (2011; Zbl 1211.65164) Full Text: DOI arXiv
Johnson, Tomas; Tucker, Warwick A note on the convergence of parametrised non-resonant invariant manifolds. (English) Zbl 1209.37028 Qual. Theory Dyn. Syst. 10, No. 1, 107-121 (2011). MSC: 37D10 34C45 34C20 37M99 65G20 PDFBibTeX XMLCite \textit{T. Johnson} and \textit{W. Tucker}, Qual. Theory Dyn. Syst. 10, No. 1, 107--121 (2011; Zbl 1209.37028) Full Text: DOI arXiv
Foryś, Wit; Oprocha, Piotr; Bakalarski, Slawomir Symbolic dynamics, flower automata and infinite traces. (English) Zbl 1226.68053 Domaratzki, Michael (ed.) et al., Implementation and application of automata. 15th international conference, CIAA 2010, Winnipeg, MB, Canada, August 12–15, 2010. Revised selected papers. Berlin: Springer (ISBN 978-3-642-18097-2/pbk). Lecture Notes in Computer Science 6482, 135-142 (2011). MSC: 68Q85 37B10 68N30 68Q45 PDFBibTeX XMLCite \textit{W. Foryś} et al., Lect. Notes Comput. Sci. 6482, 135--142 (2011; Zbl 1226.68053) Full Text: DOI
Mireles James, J. D. Adaptive set-oriented computation of topological horseshoe factors in area and volume preserving maps. (English) Zbl 1201.65217 SIAM J. Appl. Dyn. Syst. 9, No. 4, 1164-1200 (2010). MSC: 65P20 65G20 37B10 37B30 37C05 37C29 37C50 37D45 PDFBibTeX XMLCite \textit{J. D. Mireles James}, SIAM J. Appl. Dyn. Syst. 9, No. 4, 1164--1200 (2010; Zbl 1201.65217) Full Text: DOI
Bournez, Olivier; Graça, Daniel S.; Hainry, Emmanuel Robust computations with dynamical systems. (English) Zbl 1287.68103 Hliněný, Petr (ed.) et al., Mathematical foundations of computer science 2010. 35th international symposium, MFCS 2010, Brno, Czech Republic, August 23–27, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-15154-5/pbk). Lecture Notes in Computer Science 6281, 198-208 (2010). MSC: 68Q60 03D78 37C99 37N99 68Q10 PDFBibTeX XMLCite \textit{O. Bournez} et al., Lect. Notes Comput. Sci. 6281, 198--208 (2010; Zbl 1287.68103) Full Text: DOI
van den Berg, Jan Bouwe; Lessard, Jean-Philippe; Mischaikow, Konstantin Global smooth solution curves using rigorous branch following. (English) Zbl 1206.37045 Math. Comput. 79, No. 271, 1565-1584 (2010). Reviewer: Fuhua Ling (Milpitas) MSC: 37M99 65G20 65N30 PDFBibTeX XMLCite \textit{J. B. van den Berg} et al., Math. Comput. 79, No. 271, 1565--1584 (2010; Zbl 1206.37045) Full Text: DOI
Johnson, Tomas Computer-aided computation of abelian integrals and robust normal forms. (English) Zbl 1514.65002 Uppsala Dissertations in Mathematics 66. Uppsala: Uppsala Univ., Department of Mathematics (Diss.) (ISBN 978-91-506-2093-1). vi, 24 p., open access (2009). MSC: 65-02 65D17 34A60 34C07 34C20 37D10 37G15 37M20 37M99 65G20 65L09 65L70 PDFBibTeX XMLCite \textit{T. Johnson}, Computer-aided computation of abelian integrals and robust normal forms. Uppsala: Uppsala Univ., Department of Mathematics (Diss.) (2009; Zbl 1514.65002) Full Text: Link
Shen, Liyong; Wu, Min; Yang, Zhengfeng; Zeng, Zhenbing Finding positively invariant sets of a class of nonlinear loops via curve fitting. (English) Zbl 1356.68147 Kai, Hiroshi (ed.) et al., Proceedings of the 2009 workshop on symbolic-numeric computation, SNC 2009, Kyoto, Japan, August 3–5, 2009. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-60558-664-9). 185-190 (2009). MSC: 68Q60 37D45 65D10 PDFBibTeX XMLCite \textit{L. Shen} et al., in: Proceedings of the 2009 workshop on symbolic-numeric computation, SNC 2009, Kyoto, Japan, August 3--5, 2009. New York, NY: Association for Computing Machinery (ACM). 185--190 (2009; Zbl 1356.68147) Full Text: DOI
Taly, Ankur; Tiwari, Ashish Deductive verification of continuous dynamical systems. (English) Zbl 1248.68336 Kannan, Ravi (ed.) et al., IARCS annual conference on foundations of software technology and theoretical computer science (FSTTCS 2009), December 15–17, 2009, Kanpur, India. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-939897-13-2). LIPIcs – Leibniz International Proceedings in Informatics 4, 383-394, electronic only (2009). MSC: 68Q60 68Q85 37N99 37C10 PDFBibTeX XMLCite \textit{A. Taly} and \textit{A. Tiwari}, LIPIcs -- Leibniz Int. Proc. Inform. 4, 383--394 (2009; Zbl 1248.68336) Full Text: DOI Link
Moss, Robert; Kazmierczak, Ed; Kirley, Michael; Harris, Peter A computational model for emergent dynamics in the kidney. (English) Zbl 1185.37193 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 367, No. 1896, 2125-2140 (2009). MSC: 37N25 68Q60 92C50 PDFBibTeX XMLCite \textit{R. Moss} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 367, No. 1896, 2125--2140 (2009; Zbl 1185.37193) Full Text: DOI
Acedo, L. A cellular automaton model for collective neural dynamics. (English) Zbl 1185.68404 Math. Comput. Modelling 50, No. 5-6, 717-725 (2009). MSC: 68Q60 92D10 37N25 PDFBibTeX XMLCite \textit{L. Acedo}, Math. Comput. Modelling 50, No. 5--6, 717--725 (2009; Zbl 1185.68404) Full Text: DOI
Johnson, Tomas; Tucker, Warwick A rigorous study of possible configurations of limit cycles bifurcating from a hyper-elliptic Hamiltonian of degree five. (English) Zbl 1175.37055 Dyn. Syst. 24, No. 2, 237-247 (2009). Reviewer: Iliya Iliev (Sofia) MSC: 37G15 37M20 34C07 65G20 PDFBibTeX XMLCite \textit{T. Johnson} and \textit{W. Tucker}, Dyn. Syst. 24, No. 2, 237--247 (2009; Zbl 1175.37055) Full Text: DOI
Li, Zhaohong; Hou, Jianjun; Song, Wei On a binary document image authentication watermarking technique based on hierarchical structures. (Chinese. English summary) Zbl 1174.68747 Acta Autom. Sin. 34, No. 8, 841-848 (2008). MSC: 68U10 94A08 37D45 PDFBibTeX XMLCite \textit{Z. Li} et al., Acta Autom. Sin. 34, No. 8, 841--848 (2008; Zbl 1174.68747) Full Text: DOI
Barrett, Chris; Hunt, Harry B. III; Marathe, Madhav V.; Ravi, S. S.; Rosenkrantz, Daniel J.; Stearns, Richard E.; Thakur, Mayur Errata for the paper “Predecessor existence problems for finite discrete dynamical systems”. (English) Zbl 1138.68426 Theor. Comput. Sci. 395, No. 1, 132-133 (2008). MSC: 68Q25 68Q17 37B15 68Q60 68Q80 PDFBibTeX XMLCite \textit{C. Barrett} et al., Theor. Comput. Sci. 395, No. 1, 132--133 (2008; Zbl 1138.68426) Full Text: DOI
Korovina, Margarita; Vorobjov, Nicolai Satisfiability of viability constraints for Pfaffian dynamics. (English) Zbl 1185.68447 Virbitskaite, Irina (ed.) et al., Perspectives of systems informatics. 6th international Andrei Ershov memorial conference, PSI 2006, Novosibirsk, Russia, June 27–30, 2006. Revised papers. Berlin: Springer (ISBN 978-3-540-70880-3/pbk). Lecture Notes in Computer Science 4378, 260-269 (2007). MSC: 68Q85 37B10 68Q60 PDFBibTeX XMLCite \textit{M. Korovina} and \textit{N. Vorobjov}, Lect. Notes Comput. Sci. 4378, 260--269 (2007; Zbl 1185.68447) Full Text: DOI
Chua, Leon O.; Karacs, Kristof; Sbitnev, Valery I.; Guan, Junbiao; Shin, Jinwook A nonlinear dynamics perspective of Wolfram’s new kind of science. VIII: More Isles of Eden. (English) Zbl 1151.37302 Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 11, 3741-3894 (2007). MSC: 37B15 37-01 37B10 37N20 68Q60 PDFBibTeX XMLCite \textit{L. O. Chua} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 11, 3741--3894 (2007; Zbl 1151.37302) Full Text: DOI
Chua, Leon O.; Guan, Junbiao; Sbitnev, Valery I.; Shin, Jinwook A nonlinear dynamics perspective of Wolfram’s new kind of science. VII: Isles of Eden. (English) Zbl 1146.37012 Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 9, 2839-3012 (2007). Reviewer: Thomas Ward (Norwich) MSC: 37B15 37-01 37B10 37N20 68Q60 PDFBibTeX XMLCite \textit{L. O. Chua} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 9, 2839--3012 (2007; Zbl 1146.37012) Full Text: DOI
Hiraoka, Yasuaki Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems. (English) Zbl 1138.65107 Kybernetika 43, No. 6, 797-806 (2007). MSC: 65P30 37C29 37G15 37M20 65G20 PDFBibTeX XMLCite \textit{Y. Hiraoka}, Kybernetika 43, No. 6, 797--806 (2007; Zbl 1138.65107) Full Text: EuDML Link
Raimondi, A.; Tebaldi, C. Competitive logistic networks with adaption. (English) Zbl 1135.37347 Int. J. Pure Appl. Math. 42, No. 2, 275-280 (2007). MSC: 37N99 68T05 68Q60 94C05 PDFBibTeX XMLCite \textit{A. Raimondi} and \textit{C. Tebaldi}, Int. J. Pure Appl. Math. 42, No. 2, 275--280 (2007; Zbl 1135.37347)
Chua, Leon O. A nonlinear dynamics perspective of Wolfram’s new kind of science. Vol. 2. (English) Zbl 1135.37001 World Scientific Series on Nonlinear Science. Series A 57. Hackensack, NJ: World Scientific (ISBN 981-256-976-6/hbk; 981-256-642-2/set; 978-981-277-213-8/ebook). i-xviii, 369-947. (2007). Reviewer: Thomas Ward (Norwich) MSC: 37-01 37B10 37N20 37B15 68Q60 PDFBibTeX XMLCite \textit{L. O. Chua}, A nonlinear dynamics perspective of Wolfram's new kind of science. Vol. 2. Hackensack, NJ: World Scientific (2007; Zbl 1135.37001)
Barrett, Chris; Hunt, Harry B. III; Marathe, Madhav V.; Ravi, S. S.; Rosenkrantz, Daniel J.; Stearns, Richard E.; Thakur, Mayur Predecessor existence problems for finite discrete dynamical systems. (English) Zbl 1137.68410 Theor. Comput. Sci. 386, No. 1-2, 3-37 (2007); errata ibid. 395, No. 1, 132-133 (2008). MSC: 68Q25 68Q17 37B15 68Q60 68Q80 PDFBibTeX XMLCite \textit{C. Barrett} et al., Theor. Comput. Sci. 386, No. 1--2, 3--37 (2007; Zbl 1137.68410) Full Text: DOI
Kokubu, Hiroshi; Wilczak, Daniel; Zgliczyński, Piotr Rigorous verification of cocoon bifurcations in the Michelson system. (English) Zbl 1126.37035 Nonlinearity 20, No. 9, 2147-2174 (2007). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 37G15 34C37 37G40 65G20 PDFBibTeX XMLCite \textit{H. Kokubu} et al., Nonlinearity 20, No. 9, 2147--2174 (2007; Zbl 1126.37035) Full Text: DOI
Martynov, R. S. Experimental verification of a theoretical error estimate for calculation of a response matrix. (English) Zbl 1124.65116 Russ. J. Numer. Anal. Math. Model. 22, No. 3, 221-231 (2007). MSC: 65P10 37H05 PDFBibTeX XMLCite \textit{R. S. Martynov}, Russ. J. Numer. Anal. Math. Model. 22, No. 3, 221--231 (2007; Zbl 1124.65116)
Wilczak, Daniel; Zgliczyński, Piotr Topological method for symmetric periodic orbits for maps with a reversing symmetry. (English) Zbl 1124.37015 Discrete Contin. Dyn. Syst. 17, No. 3, 629-652 (2007). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 37C80 37C25 65G20 PDFBibTeX XMLCite \textit{D. Wilczak} and \textit{P. Zgliczyński}, Discrete Contin. Dyn. Syst. 17, No. 3, 629--652 (2007; Zbl 1124.37015) Full Text: DOI arXiv
Skokos, Ch.; Bountis, T. C.; Antonopoulos, Ch. Geometrical properties of local dynamics in Hamiltonian systems: the generalized alignment index (GALI) method. (English) Zbl 1117.37034 Physica D 231, No. 1, 30-54 (2007). MSC: 37J45 37D45 37M25 PDFBibTeX XMLCite \textit{Ch. Skokos} et al., Physica D 231, No. 1, 30--54 (2007; Zbl 1117.37034) Full Text: DOI arXiv
Mönnigmann, Martin; Marquardt, Wolfgang; Bischof, Christian H.; Beelitz, Thomas; Lang, Bruno; Willems, Paul A hybrid approach for efficient robust design of dynamic systems. (English) Zbl 1114.93034 SIAM Rev. 49, No. 2, 236-254 (2007). MSC: 93B51 37N35 65G20 65H10 90C30 PDFBibTeX XMLCite \textit{M. Mönnigmann} et al., SIAM Rev. 49, No. 2, 236--254 (2007; Zbl 1114.93034) Full Text: DOI
Hiraoka, Yasuaki; Ogawa, Toshiyuki An efficient estimate based on FFT in topological verification method. (English) Zbl 1109.65110 J. Comput. Appl. Math. 199, No. 2, 238-244 (2007). MSC: 65P30 37B30 35Q35 65M70 35B32 37K50 65T50 PDFBibTeX XMLCite \textit{Y. Hiraoka} and \textit{T. Ogawa}, J. Comput. Appl. Math. 199, No. 2, 238--244 (2007; Zbl 1109.65110) Full Text: DOI
Viswanath, K. Computing with dynamical systems. (English) Zbl 1128.68119 Differ. Equ. Dyn. Syst. 14, No. 1-2, 1-25 (2006). Reviewer: Werner M. Seiler (Kassel) MSC: 68W40 37N99 68Q05 37M99 37B99 37N30 39B12 PDFBibTeX XMLCite \textit{K. Viswanath}, Differ. Equ. Dyn. Syst. 14, No. 1--2, 1--25 (2006; Zbl 1128.68119)
Fundinger, Danny Investigating dynamics by symbolic analysis: tunings for an efficient computation of the symbolic image. (English) Zbl 1479.37081 Differ. Uravn. Protsessy Upr. 2005, No. 3, 16-37 (2005). MSC: 37M05 PDFBibTeX XMLCite \textit{D. Fundinger}, Differ. Uravn. Protsessy Upr. 2005, No. 3, 16--37 (2005; Zbl 1479.37081) Full Text: Link
Hiraoka, Yasuaki; Ogawa, Toshiyuki Rigorous numerics for localized patterns to the quintic Swift-Hohenberg equation. (English) Zbl 1067.65146 Japan J. Ind. Appl. Math. 22, No. 1, 57-75 (2005). MSC: 65P30 37K50 37M20 PDFBibTeX XMLCite \textit{Y. Hiraoka} and \textit{T. Ogawa}, Japan J. Ind. Appl. Math. 22, No. 1, 57--75 (2005; Zbl 1067.65146) Full Text: DOI
Hamdi, S.; Enright, W. H.; Ouellet, Y.; Schiesser, W. E. Exact solutions of extended Boussinesq equations. (English) Zbl 1075.74565 Numer. Algorithms 37, No. 1-4, 165-175 (2004). MSC: 74J30 35Q53 35C05 74J35 37K05 PDFBibTeX XMLCite \textit{S. Hamdi} et al., Numer. Algorithms 37, No. 1--4, 165--175 (2004; Zbl 1075.74565) Full Text: DOI
Osipenko, G. S.; Schanz, M.; Ershov, E. K. Test for hyperbolicity of a dynamical system. (English) Zbl 1244.37021 Osipenko, G. S. (ed.), Tools for mathematical modelling. Proceedings of the 4th international conference, St. Petersburg, Russia, June 23–28, 2003. St. Petersburg: St. Petersburg State Polytechnic University (ISBN 5-7422-0511-2/pbk). Math. Res., St. Petersburg 9, 338-344 (2003). MSC: 37D20 37D25 05C90 37B10 PDFBibTeX XMLCite \textit{G. S. Osipenko} et al., Math. Res., St. Petersburg 9, 338--344 (2003; Zbl 1244.37021)
De Feo, Oscar; Maggio, Gian Mario Bifurcations in the Colpitts oscillator: from theory to practice. (English) Zbl 1099.37508 Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 10, 2917-2934 (2003). MSC: 37G15 34C23 37D45 94C05 PDFBibTeX XMLCite \textit{O. De Feo} and \textit{G. M. Maggio}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 10, 2917--2934 (2003; Zbl 1099.37508) Full Text: DOI
Zgliczynski, Piotr \(C^1\) Lohner algorithm. (English) Zbl 1049.65038 Found. Comput. Math. 2, No. 4, 429-465 (2002). MSC: 65G20 34A45 37M99 65L05 PDFBibTeX XMLCite \textit{P. Zgliczynski}, Found. Comput. Math. 2, No. 4, 429--465 (2002; Zbl 1049.65038) Full Text: DOI
Zgliczynski, Piotr Attracting fixed points for the Kuramoto–Sivashinsky equation: A computer assisted proof. (English) Zbl 1004.35017 SIAM J. Appl. Dyn. Syst. 1, No. 2, 215-235 (2002). MSC: 35B35 37L65 65G20 65N30 35B45 PDFBibTeX XMLCite \textit{P. Zgliczynski}, SIAM J. Appl. Dyn. Syst. 1, No. 2, 215--235 (2002; Zbl 1004.35017) Full Text: DOI
Du, Zhengdong; Hassard, Brian Precise computation of Hopf bifurcation and two applications. (English) Zbl 1002.37041 Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 8, No. 4, 495-518 (2001). Reviewer: Ale Jan Homburg (Amsterdam) MSC: 37M20 65P30 92C45 34C23 37Gxx 65G20 65G40 PDFBibTeX XMLCite \textit{Z. Du} and \textit{B. Hassard}, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 8, No. 4, 495--518 (2001; Zbl 1002.37041)