Sansottera, Marco; Danesi, Veronica Kolmogorov variation: Kam with knobs (à la Kolmogorov). (English) Zbl 07817724 Math. Eng. (Springfield) 5, No. 5, Paper No. 89, 19 p. (2023). MSC: 68-XX 65-XX PDFBibTeX XMLCite \textit{M. Sansottera} and \textit{V. Danesi}, Math. Eng. (Springfield) 5, No. 5, Paper No. 89, 19 p. (2023; Zbl 07817724) Full Text: DOI arXiv
Fortunati, Alessandro On the constructivity of the variational approach to Arnold’s Diffusion. arXiv:2306.11834 Preprint, arXiv:2306.11834 [math.DS] (2023). MSC: 37J40 37J50 65K10 70H08 BibTeX Cite \textit{A. Fortunati}, ``On the constructivity of the variational approach to Arnold's Diffusion'', Preprint, arXiv:2306.11834 [math.DS] (2023) Full Text: arXiv OA License
Daquin, Jérôme; Pédenon-Orlanducci, Rémi; Agaoglou, Makrina; García-Sánchez, Guillermo; Mancho, Ana Maria Global dynamics visualisation from Lagrangian descriptors. Applications to discrete and continuous systems. (English) Zbl 1511.37103 Physica D 442, Article ID 133520, 14 p. (2022). Reviewer: Christian Pötzsche (Klagenfurt) MSC: 37M25 37M15 65P10 70K43 70H08 PDFBibTeX XMLCite \textit{J. Daquin} et al., Physica D 442, Article ID 133520, 14 p. (2022; Zbl 1511.37103) Full Text: DOI arXiv
Zheng, Hang; Xia, Yonghui; Pinto, Manuel Chaotic motion and control of the driven-damped double sine-Gordon equation. (English) Zbl 1505.34065 Discrete Contin. Dyn. Syst., Ser. B 27, No. 12, 7151-7167 (2022). MSC: 34C28 34C37 34H10 65P20 35L10 35C07 37J40 PDFBibTeX XMLCite \textit{H. Zheng} et al., Discrete Contin. Dyn. Syst., Ser. B 27, No. 12, 7151--7167 (2022; Zbl 1505.34065) Full Text: DOI
González, Alejandra; Haro, Àlex; de la Llave, Rafael Efficient and reliable algorithms for the computation of non-twist invariant circles. (English) Zbl 1501.37064 Found. Comput. Math. 22, No. 3, 791-847 (2022). MSC: 37J40 37J20 37M20 65T50 PDFBibTeX XMLCite \textit{A. González} et al., Found. Comput. Math. 22, No. 3, 791--847 (2022; Zbl 1501.37064) Full Text: DOI
Nieto, Alexandre R.; Seoane, Jesús M.; Sanjuán, Miguel A. F. Noise activates escapes in closed Hamiltonian systems. (English) Zbl 1485.37058 Commun. Nonlinear Sci. Numer. Simul. 105, Article ID 106074, 12 p. (2022). MSC: 37J40 37M22 65P20 70K55 PDFBibTeX XMLCite \textit{A. R. Nieto} et al., Commun. Nonlinear Sci. Numer. Simul. 105, Article ID 106074, 12 p. (2022; Zbl 1485.37058) Full Text: DOI arXiv
Cárcamo-Díaz, Daniela; Palacián, Jesús F.; Vidal, Claudio; Yanguas, Patricia Nonlinear stability in the spatial attitude motion of a satellite in a circular orbit. (English) Zbl 1481.37105 SIAM J. Appl. Dyn. Syst. 20, No. 3, 1421-1463 (2021). MSC: 37N05 37J25 37J40 70F15 70K28 65L70 PDFBibTeX XMLCite \textit{D. Cárcamo-Díaz} et al., SIAM J. Appl. Dyn. Syst. 20, No. 3, 1421--1463 (2021; Zbl 1481.37105) Full Text: DOI
Caracciolo, Chiara; Locatelli, Ugo Elliptic tori in FPU non-linear chains with a small number of nodes. (English) Zbl 1462.37072 Commun. Nonlinear Sci. Numer. Simul. 97, Article ID 105759, 23 p. (2021). MSC: 37J40 37N05 37K60 65P40 70H08 70H15 PDFBibTeX XMLCite \textit{C. Caracciolo} and \textit{U. Locatelli}, Commun. Nonlinear Sci. Numer. Simul. 97, Article ID 105759, 23 p. (2021; Zbl 1462.37072) Full Text: DOI arXiv
Modin, Klas; Verdier, Olivier What makes nonholonomic integrators work? (English) Zbl 1447.37068 Numer. Math. 145, No. 2, 405-435 (2020). Reviewer: Bülent Karasözen (Ankara) MSC: 37M15 65P10 37J60 37J40 70F25 37N30 65D30 37J35 PDFBibTeX XMLCite \textit{K. Modin} and \textit{O. Verdier}, Numer. Math. 145, No. 2, 405--435 (2020; Zbl 1447.37068) Full Text: DOI arXiv
Le, Uyen; Pelinovsky, Dmitry E. Convergence of Petviashvili’s method near periodic waves in the fractional Korteweg-de Vries equation. (English) Zbl 1419.35178 SIAM J. Math. Anal. 51, No. 4, 2850-2883 (2019). MSC: 35Q53 35P30 37K50 37K55 65J15 PDFBibTeX XMLCite \textit{U. Le} and \textit{D. E. Pelinovsky}, SIAM J. Math. Anal. 51, No. 4, 2850--2883 (2019; Zbl 1419.35178) Full Text: DOI arXiv
Ding, Zhaodong; Shang, Zaijiu Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems. (English) Zbl 1400.37068 Sci. China, Math. 61, No. 9, 1567-1588 (2018). MSC: 37J40 37J35 65L07 65L20 65P10 65P40 37J10 70K43 PDFBibTeX XMLCite \textit{Z. Ding} and \textit{Z. Shang}, Sci. China, Math. 61, No. 9, 1567--1588 (2018; Zbl 1400.37068) Full Text: DOI arXiv
Gelfreich, V.; Vieiro, A. Interpolating vector fields for near identity maps and averaging. (English) Zbl 1406.37059 Nonlinearity 31, No. 9, 4263-4289 (2018). Reviewer: Fernando Casas (Castellon) MSC: 37M15 65P10 37J40 34K33 PDFBibTeX XMLCite \textit{V. Gelfreich} and \textit{A. Vieiro}, Nonlinearity 31, No. 9, 4263--4289 (2018; Zbl 1406.37059) Full Text: DOI arXiv Link
Canadell, Marta; Haro, Àlex Computation of quasiperiodic normally hyperbolic invariant tori: rigorous results. (English) Zbl 1380.37061 J. Nonlinear Sci. 27, No. 6, 1869-1904 (2017). MSC: 37D10 37E45 37J40 37M25 65P40 PDFBibTeX XMLCite \textit{M. Canadell} and \textit{À. Haro}, J. Nonlinear Sci. 27, No. 6, 1869--1904 (2017; Zbl 1380.37061) 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
Delshams, Amadeu; Gidea, Marian; Roldan, Pablo Arnold’s mechanism of diffusion in the spatial circular restricted three-body problem: A semi-analytical argument. (English) Zbl 1415.70019 Physica D 334, 29-48 (2016). MSC: 70F07 37J40 37C50 37M05 65P10 PDFBibTeX XMLCite \textit{A. Delshams} et al., Physica D 334, 29--48 (2016; Zbl 1415.70019) Full Text: DOI
Bilman, D.; Nenciu, I. On the evolution of scattering data under perturbations of the Toda lattice. (English) Zbl 1373.37154 Physica D 330, 1-16 (2016). MSC: 37K10 37K55 37M05 65P99 PDFBibTeX XMLCite \textit{D. Bilman} and \textit{I. Nenciu}, Physica D 330, 1--16 (2016; Zbl 1373.37154) Full Text: DOI arXiv
Luque, Alejandro; Villanueva, Jordi A numerical method for computing initial conditions of Lagrangian invariant tori using the frequency map. (English) Zbl 1364.65283 Physica D 325, 63-73 (2016). MSC: 65P10 37J40 PDFBibTeX XMLCite \textit{A. Luque} and \textit{J. Villanueva}, Physica D 325, 63--73 (2016; Zbl 1364.65283) Full Text: DOI Link
McLachlan, Robert I.; Modin, Klas; Verdier, Olivier Geometry of discrete-time spin systems. (English) Zbl 1352.37190 J. Nonlinear Sci. 26, No. 5, 1507-1523 (2016). MSC: 37M15 65P10 70H08 37J35 PDFBibTeX XMLCite \textit{R. I. McLachlan} et al., J. Nonlinear Sci. 26, No. 5, 1507--1523 (2016; Zbl 1352.37190) Full Text: DOI arXiv
Soga, Kohei More on stochastic and variational approach to the Lax-Friedrichs scheme. (English) Zbl 1342.65176 Math. Comput. 85, No. 301, 2161-2193 (2016). Reviewer: Marius Ghergu (Dublin) MSC: 65M06 35L65 37K55 35F21 65M12 65M15 PDFBibTeX XMLCite \textit{K. Soga}, Math. Comput. 85, No. 301, 2161--2193 (2016; Zbl 1342.65176) Full Text: DOI arXiv
Fox, Adam M.; Meiss, James D. Computing the conjugacy of invariant tori for volume-preserving maps. (English) Zbl 1381.37064 SIAM J. Appl. Dyn. Syst. 15, No. 1, 557-579 (2016). Reviewer: Vasile Marinca (Timişoara) MSC: 37J15 37J40 70K43 70K55 42B10 65P10 PDFBibTeX XMLCite \textit{A. M. Fox} and \textit{J. D. Meiss}, SIAM J. Appl. Dyn. Syst. 15, No. 1, 557--579 (2016; Zbl 1381.37064) Full Text: DOI
Dosso, Mouhamadou; Coulibaly, Namory An analysis of the behavior of multipliers of Hamiltonian system with periodic coefficients. (English) Zbl 1334.37066 Far East J. Math. Sci. (FJMS) 99, No. 3, 301-322 (2016). MSC: 37J40 37M05 65F15 93C15 37N35 PDFBibTeX XMLCite \textit{M. Dosso} and \textit{N. Coulibaly}, Far East J. Math. Sci. (FJMS) 99, No. 3, 301--322 (2016; Zbl 1334.37066) Full Text: DOI Link
Fox, Adam M.; de la Llave, Rafael Barriers to transport and mixing in volume-preserving maps with nonzero flux. (English) Zbl 1364.76066 Physica D 295-296, 1-10 (2015). MSC: 76F25 65P99 37J40 37N10 37M05 PDFBibTeX XMLCite \textit{A. M. Fox} and \textit{R. de la Llave}, Physica D 295--296, 1--10 (2015; Zbl 1364.76066) Full Text: DOI arXiv
Harsoula, M.; Contopoulos, G.; Efthymiopoulos, C. Analytical description of the structure of chaos. (English) Zbl 1365.37048 J. Phys. A, Math. Theor. 48, No. 13, Article ID 135102, 20 p. (2015). MSC: 37J10 37M20 37J40 37J35 65P20 PDFBibTeX XMLCite \textit{M. Harsoula} et al., J. Phys. A, Math. Theor. 48, No. 13, Article ID 135102, 20 p. (2015; Zbl 1365.37048) Full Text: DOI arXiv
Modin, Klas; Verdier, Olivier Integrability of nonholonomically coupled oscillators. (English) Zbl 1368.70023 Discrete Contin. Dyn. Syst. 34, No. 3, 1121-1130 (2014). MSC: 70F25 37J60 37M15 65P99 70H08 PDFBibTeX XMLCite \textit{K. Modin} and \textit{O. Verdier}, Discrete Contin. Dyn. Syst. 34, No. 3, 1121--1130 (2014; Zbl 1368.70023) Full Text: DOI arXiv
Moan, Per Christian; Niesen, Jitse On an asymptotic method for computing the modified energy for symplectic methods. (English) Zbl 1277.65107 Discrete Contin. Dyn. Syst. 34, No. 3, 1105-1120 (2014). MSC: 65P10 37J40 37M15 PDFBibTeX XMLCite \textit{P. C. Moan} and \textit{J. Niesen}, Discrete Contin. Dyn. Syst. 34, No. 3, 1105--1120 (2014; Zbl 1277.65107) Full Text: DOI arXiv Link
Cordani, Bruno Geography of order and chaos in mechanics. Investigations of quasi-integrable systems with analytical, numerical, and graphical tools. (English) Zbl 1258.70001 Progress in Mathematical Physics 64. New York: Birkhäuser (ISBN 978-0-8176-8369-6/hbk; 978-0-8176-8370-2/ebook). xviii, 332 p. (2013). Reviewer: Nicolas Roy (Berlin) MSC: 70-01 37J40 70F15 37J05 70H08 70H33 65P10 37J15 37N05 37M10 65L06 PDFBibTeX XMLCite \textit{B. Cordani}, Geography of order and chaos in mechanics. Investigations of quasi-integrable systems with analytical, numerical, and graphical tools. New York: Birkhäuser (2013; Zbl 1258.70001) Full Text: DOI
Huguet, Gemma; de la Llave, Rafael; Sire, Yannick Computation of whiskered invariant tori and their associated manifolds: new fast algorithms. (English) Zbl 1279.70004 Discrete Contin. Dyn. Syst. 32, No. 4, 1309-1353 (2012). MSC: 70-08 70H08 37M99 65P10 PDFBibTeX XMLCite \textit{G. Huguet} et al., Discrete Contin. Dyn. Syst. 32, No. 4, 1309--1353 (2012; Zbl 1279.70004) Full Text: DOI arXiv
Privault, Nicolas; Zambrini, Jean-Claude Stochastic deformation of integrable dynamical systems and random time symmetry. (English) Zbl 1312.70010 J. Math. Phys. 51, No. 8, 082104, 19 p. (2010). MSC: 70H06 37J40 60J60 70H03 70H05 70H20 70H25 35A30 65M25 PDFBibTeX XMLCite \textit{N. Privault} and \textit{J.-C. Zambrini}, J. Math. Phys. 51, No. 8, 082104, 19 p. (2010; Zbl 1312.70010) Full Text: DOI Link
Gauckler, Ludwig; Lubich, Christian Nonlinear Schrödinger equations and their spectral semi-discretizations over long times. (English) Zbl 1194.37121 Found. Comput. Math. 10, No. 2, 141-169 (2010). Reviewer: Hu Chuangan (Cupertino) MSC: 37K55 65M70 35Q55 PDFBibTeX XMLCite \textit{L. Gauckler} and \textit{C. Lubich}, Found. Comput. Math. 10, No. 2, 141--169 (2010; Zbl 1194.37121) Full Text: DOI
Le Bris, Claude; Legoll, Frédéric Integrators for highly oscillatory Hamiltonian systems: an homogenization approach. (English) Zbl 1259.37051 Discrete Contin. Dyn. Syst., Ser. B 13, No. 2, 347-373 (2010). MSC: 37M15 37J40 65P10 65P40 70H20 70K70 74Q10 PDFBibTeX XMLCite \textit{C. Le Bris} and \textit{F. Legoll}, Discrete Contin. Dyn. Syst., Ser. B 13, No. 2, 347--373 (2010; Zbl 1259.37051) Full Text: DOI
McLachlan, Robert I.; O’Neale, Dion R. J. Preservation and destruction of periodic orbits by symplectic integrators. (English) Zbl 1196.65191 Numer. Algorithms 53, No. 2-3, 343-362 (2010). Reviewer: Josep J. Masdemont (Barcelona) MSC: 65P10 PDFBibTeX XMLCite \textit{R. I. McLachlan} and \textit{D. R. J. O'Neale}, Numer. Algorithms 53, No. 2--3, 343--362 (2010; Zbl 1196.65191) Full Text: DOI
Feng, Kang; Qin, Mengzhao Symplectic geometric algorithms for Hamiltonian systems. With a foreword by Feng Duan and a preface by Qin, Mengzhao. (English) Zbl 1207.65149 Hangzhou: Zhejiang Publishing United Group, Zhejiang Science and Technology Publishing House; Berlin: Springer (ISBN 978-7-5341-3595-8; 978-3-642-01776-6/hbk). xxiii, 676 p. (2010). Reviewer: Kevin Burrage (Brisbane) MSC: 65P10 65-02 65L06 37J40 37J05 37M15 37K05 37K55 PDFBibTeX XMLCite \textit{K. Feng} and \textit{M. Qin}, Symplectic geometric algorithms for Hamiltonian systems. With a foreword by Feng Duan and a preface by Qin, Mengzhao. Hangzhou: Zhejiang Publishing United Group, Zhejiang Science and Technology Publishing House; Berlin: Springer (2010; Zbl 1207.65149) Full Text: DOI
Skeel, Robert D. What makes molecular dynamics work? (English) Zbl 1208.37037 SIAM J. Sci. Comput. 31, No. 2, 1363-1378 (2009). Reviewer: Adriana Buică (Cluj-Napoca) MSC: 37J40 37M15 37N99 65L20 65P10 65Z05 82B05 82C05 PDFBibTeX XMLCite \textit{R. D. Skeel}, SIAM J. Sci. Comput. 31, No. 2, 1363--1378 (2009; Zbl 1208.37037) Full Text: DOI Link
Hairer, Ernst; Lubich, Christian Oscillation over long times in numerical Hamiltonian systems. (English) Zbl 1180.37121 Engquist, Bjorn (ed.) et al., Highly oscillatory problems. Cambridge: Cambridge University Press (ISBN 978-0-521-13443-9/pbk). London Mathematical Society Lecture Note Series 366, 1-24 (2009). MSC: 37M05 37M15 65P10 65L05 65L06 34C15 37J40 PDFBibTeX XMLCite \textit{E. Hairer} and \textit{C. Lubich}, Lond. Math. Soc. Lect. Note Ser. 366, 1--24 (2009; Zbl 1180.37121)
Castella, François; Dujardin, Guillaume Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation. (English) Zbl 1171.65089 ESAIM, Math. Model. Numer. Anal. 43, No. 4, 651 (2009). Reviewer: Qin Mengzhao (Beijing) MSC: 65P10 37K55 37M15 35J10 PDFBibTeX XMLCite \textit{F. Castella} and \textit{G. Dujardin}, ESAIM, Math. Model. Numer. Anal. 43, No. 4, 651 (2009; Zbl 1171.65089) Full Text: DOI EuDML
Kaasalainen, Mikko Dynamical tomography of gravitationally bound systems. (English) Zbl 1177.35252 Inverse Probl. Imaging 2, No. 4, 527-546 (2008). MSC: 35R30 37J35 37J40 65C05 70H06 70K43 85A05 PDFBibTeX XMLCite \textit{M. Kaasalainen}, Inverse Probl. Imaging 2, No. 4, 527--546 (2008; Zbl 1177.35252) Full Text: DOI arXiv
Falcone, M.; Rorro, M. On a variational approximation of the effective Hamiltonian. (English) Zbl 1188.65164 Kunisch, Karl (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10–14, 2007. Berlin: Springer (ISBN 978-3-540-69776-3/hbk). 719-726 (2008). MSC: 65P10 37M15 37K55 PDFBibTeX XMLCite \textit{M. Falcone} and \textit{M. Rorro}, in: Numerical mathematics and advanced applications. Proceedings of ENUMATH 2007, the 7th European conference on numerical mathematics and advanced applications, Graz, Austria, September 10--14, 2007. Berlin: Springer. 719--726 (2008; Zbl 1188.65164)
Bogdanov, R. I.; Bogdanov, M. R. The weakly dissipative version of the Kolmogorov-Arnold-Moser theory and practical calculations. (Russian, English) Zbl 1201.37092 Comput. Math. Math. Phys. 48, No. 3, 447-463 (2008); translation from Zh. Vychisl. Mat. Mat. Fiz. 48, No. 3, 473-490 (2008). MSC: 37J40 37D45 37M99 65P10 70-08 70H08 70K55 PDFBibTeX XMLCite \textit{R. I. Bogdanov} and \textit{M. R. Bogdanov}, Zh. Vychisl. Mat. Mat. Fiz. 48, No. 3, 473--490 (2008; Zbl 1201.37092); translation from Zh. Vychisl. Mat. Mat. Fiz. 48, No. 3, 473--490 (2008) Full Text: DOI
Dujardin, Guillaume; Faou, Erwan Qualitative behavior of splitting methods for the linear Schrödinger equation in molecular dynamics. (English) Zbl 1137.65063 ESAIM, Proc. 22, 234-239 (2008). MSC: 65P10 37M15 37K55 PDFBibTeX XMLCite \textit{G. Dujardin} and \textit{E. Faou}, ESAIM, Proc. 22, 234--239 (2008; Zbl 1137.65063) Full Text: DOI
Dujardin, Guillaume; Faou, Erwan Normal form and long time analysis of splitting schemes for the linear Schrödinger equation with small potential. (English) Zbl 1137.65062 Numer. Math. 108, No. 2, 223-262 (2007). Reviewer: Jialin Hong (Beijing) MSC: 65P10 37M15 37K55 PDFBibTeX XMLCite \textit{G. Dujardin} and \textit{E. Faou}, Numer. Math. 108, No. 2, 223--262 (2007; Zbl 1137.65062) Full Text: DOI
Why Newton’s method is hard for travelling waves: small denominators, KAM theory, Arnold’s linear Fourier problem, non-uniqueness, constraints and erratic failure. (English) Zbl 1107.65351 Math. Comput. Simul. 74, No. 2-3, 72-81 (2007). MSC: 65P30 35K55 37K10 37K50 37M20 65M06 PDFBibTeX XMLCite Math. Comput. Simul. 74, No. 2--3, 72--81 (2007; Zbl 1107.65351) Full Text: DOI
Haro, À.; de la Llave, R. A parametrization method for the computation of invariant tori and their whiskers in quasi-periodic maps: numerical algorithms. (English) Zbl 1296.37048 Discrete Contin. Dyn. Syst., Ser. B 6, No. 6, 1261-1300 (2006). MSC: 37J40 37M99 65P40 70K43 PDFBibTeX XMLCite \textit{À. Haro} and \textit{R. de la Llave}, Discrete Contin. Dyn. Syst., Ser. B 6, No. 6, 1261--1300 (2006; Zbl 1296.37048) Full Text: DOI
Dullin, Holger; Fassò, Francesco An algorithm for detecting directional quasi-convexity. (English) Zbl 1069.65142 BIT 44, No. 3, 571-584 (2004). Reviewer: Manuel Calvo (Zaragoza) MSC: 65P40 65P10 37J40 70K20 70K45 PDFBibTeX XMLCite \textit{H. Dullin} and \textit{F. Fassò}, BIT 44, No. 3, 571--584 (2004; Zbl 1069.65142) Full Text: DOI
Moan, Per Christian On the KAM and Nekhoroshev theorems for symplectic integrators and implications for error growth. (English) Zbl 1068.37044 Nonlinearity 17, No. 1, 67-83 (2004). Reviewer: Anna Maria Cherubini (Lecce) MSC: 37J40 37M15 70H08 65P10 PDFBibTeX XMLCite \textit{P. C. Moan}, Nonlinearity 17, No. 1, 67--83 (2004; Zbl 1068.37044) Full Text: DOI
Cong, Fuzhong The approximate decomposition of exponential order of slow-fast motions in multifrequency systems. (English) Zbl 1034.37034 J. Differ. Equations 196, No. 2, 466-480 (2004). MSC: 37J40 34E10 34A45 65L99 34A37 PDFBibTeX XMLCite \textit{F. Cong}, J. Differ. Equations 196, No. 2, 466--480 (2004; Zbl 1034.37034) Full Text: DOI
Ma, Qun; Izaguirre, Jesús A.; Skeel, Robert D. Verlet-I/R-RESPA/Impulse is limited by nonlinear instabilities. (English) Zbl 1163.65317 SIAM J. Sci. Comput. 24, No. 6, 1951-1973 (2003). MSC: 65L05 PDFBibTeX XMLCite \textit{Q. Ma} et al., SIAM J. Sci. Comput. 24, No. 6, 1951--1973 (2003; Zbl 1163.65317) Full Text: DOI
Tuwankotta, J. M.; Quispel, G. R. W. Geometric numerical integration applied to the elastic pendulum at higher-order resonance. (English) Zbl 1107.37309 J. Comput. Appl. Math. 154, No. 1, 229-242 (2003). MSC: 37M15 65P10 70H08 70-08 PDFBibTeX XMLCite \textit{J. M. Tuwankotta} and \textit{G. R. W. Quispel}, J. Comput. Appl. Math. 154, No. 1, 229--242 (2003; Zbl 1107.37309) Full Text: DOI arXiv
Mikram, Jilali; Zinoun, Fouad Normal form methods for symbolic creation of approximate solutions of nonlinear dynamical systems. (English) Zbl 0986.65123 Math. Comput. Simul. 57, No. 3-5, 253-289 (2001). MSC: 65P10 37M15 37J40 37J45 68W30 PDFBibTeX XMLCite \textit{J. Mikram} and \textit{F. Zinoun}, Math. Comput. Simul. 57, No. 3--5, 253--289 (2001; Zbl 0986.65123) Full Text: DOI
Shang, Zai-jui Resonant and Diophantine step sizes in computing invariant tori of Hamiltonian systems. (English) Zbl 1008.65092 Nonlinearity 13, No. 1, 299-308 (2000). MSC: 65P10 37M15 37K10 11J83 PDFBibTeX XMLCite \textit{Z.-j. Shang}, Nonlinearity 13, No. 1, 299--308 (2000; Zbl 1008.65092) Full Text: DOI
Mikkola, Seppo; Palmer, Phil Simple derivation of symplectic integrators with first-order correctors. (English) Zbl 0991.70003 Celest. Mech. Dyn. Astron. 77, No. 4, 305-317 (2000). Reviewer: M.Gousidou-Koutita (Thessaloniki) MSC: 70-08 70H08 70F05 65P10 PDFBibTeX XMLCite \textit{S. Mikkola} and \textit{P. Palmer}, Celest. Mech. Dyn. Astron. 77, No. 4, 305--317 (2000; Zbl 0991.70003) Full Text: DOI
Blanes, S.; Casas, F.; Ros, J. Processing symplectic methods for near-integrable Hamiltonian systems. (English) Zbl 0986.70013 Celest. Mech. Dyn. Astron. 77, No. 1, 17-36 (2000). Reviewer: Werner M.Seiler (Mannheim) MSC: 70H08 70-08 65P10 PDFBibTeX XMLCite \textit{S. Blanes} et al., Celest. Mech. Dyn. Astron. 77, No. 1, 17--36 (2000; Zbl 0986.70013) Full Text: DOI
Carletti, Timoteo; Laskar, Jacques Scaling law in the standard map critical function. Interpolating Hamiltonian and frequency map analysis. (English) Zbl 0999.37027 Nonlinearity 13, No. 6, 2033-2061 (2000). Reviewer: Rafael Ortega (Granada) MSC: 37E40 37J40 65P10 70K43 37E45 PDFBibTeX XMLCite \textit{T. Carletti} and \textit{J. Laskar}, Nonlinearity 13, No. 6, 2033--2061 (2000; Zbl 0999.37027) Full Text: DOI arXiv
Jorba, Àngel A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems. (English) Zbl 0983.37107 Exp. Math. 8, No. 2, 155-195 (1999). Reviewer: Boris V.Loginov (Ankara) MSC: 37M20 34C20 34-04 37-04 37J40 70F15 70H05 70K50 65P99 PDFBibTeX XMLCite \textit{À. Jorba}, Exp. Math. 8, No. 2, 155--195 (1999; Zbl 0983.37107) Full Text: DOI EuDML Link
Jauslin, H. R.; Govin, M.; Cibils, M. Domains of convergence of KAM type iterations for eigenvalue problems. (English) Zbl 0958.37034 Simó, Carles (ed.), Hamiltonian systems with three or more degrees of freedom. Proceedings of the NATO Advanced Study Institute, S’Agaró, Spain, June 19-30, 1995. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 426-429 (1999). MSC: 37J40 65H17 PDFBibTeX XMLCite \textit{H. R. Jauslin} et al., NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 426--429 (1999; Zbl 0958.37034)
Laskar, Jacques Introduction to frequency map analysis. (English) Zbl 0971.70006 Simó, Carles (ed.), Hamiltonian systems with three or more degrees of freedom. Proceedings of the NATO Advanced Study Institute, S’Agaró, Spain, June 19-30, 1995. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 134-150 (1999). MSC: 70-08 70H08 65P10 37N05 PDFBibTeX XMLCite \textit{J. Laskar}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 533, 134--150 (1999; Zbl 0971.70006)
Shang, Zaijiu KAM theorem of symplectic algorithms for Hamiltonian systems. (English) Zbl 0938.65149 Numer. Math. 83, No. 3, 477-496 (1999). Reviewer: M.Gousidou-Koutita (Thessaloniki) MSC: 65P10 37M15 70H08 PDFBibTeX XMLCite \textit{Z. Shang}, Numer. Math. 83, No. 3, 477--496 (1999; Zbl 0938.65149) Full Text: DOI
Gramchev, Todor; Yoshino, Masafumi Rapidly convergent iteration method for simultaneous normal forms of commuting maps. (English) Zbl 0931.65055 Math. Z. 231, No. 4, 745-770 (1999). Reviewer: Todor Gramchev (Cagliari) MSC: 65H10 65E05 32A19 PDFBibTeX XMLCite \textit{T. Gramchev} and \textit{M. Yoshino}, Math. Z. 231, No. 4, 745--770 (1999; Zbl 0931.65055) Full Text: DOI
Bi, Qinsheng; Yu, Pei Symbolic computation of normal forms for semi-simple cases. (English) Zbl 0944.65132 J. Comput. Appl. Math. 102, No. 2, 195-220 (1999). Reviewer: Boris V.Loginov (Ul’yanovsk) MSC: 65P30 37J40 37M20 34C20 34A34 68W30 PDFBibTeX XMLCite \textit{Q. Bi} and \textit{P. Yu}, J. Comput. Appl. Math. 102, No. 2, 195--220 (1999; Zbl 0944.65132) Full Text: DOI
Hairer, Ernst; Lubich, Christian Invariant tori of dissipatively perturbed Hamiltonian systems under symplectic discretization. (English) Zbl 1022.37042 Appl. Numer. Math. 29, No. 1, 57-71 (1999). MSC: 37J40 37M15 70H05 70-08 65L99 70H08 PDFBibTeX XMLCite \textit{E. Hairer} and \textit{C. Lubich}, Appl. Numer. Math. 29, No. 1, 57--71 (1999; Zbl 1022.37042) Full Text: DOI
Di Sebastiano, Annamaria; Turchetti, Giorgio Interpolation of discrete Hamiltonian systems. (English) Zbl 1088.37510 Benest, Daniel (ed.) et al., Analysis and modelling of discrete dynamical systems. Reading: Gordon and Breach (ISBN 90-5699-625-8/hbk). Adv. Discrete Math. Appl. 1, 181-227 (1998). MSC: 37J10 37J40 70-08 70H05 65P99 37C55 PDFBibTeX XMLCite \textit{A. Di Sebastiano} and \textit{G. Turchetti}, Adv. Discrete Math. Appl. 1, 181--227 (1998; Zbl 1088.37510)
Efthymiopoulos, Christos; Voglis, Nikos; Contopoulos, George Diffusion and transient spectra in a 4-dimensional symplectic mapping. (English) Zbl 1088.37511 Benest, Daniel (ed.) et al., Analysis and modelling of discrete dynamical systems. Reading: Gordon and Breach (ISBN 90-5699-625-8/hbk). Adv. Discrete Math. Appl. 1, 91-106 (1998). MSC: 37J10 37J40 65M99 65Q05 PDFBibTeX XMLCite \textit{C. Efthymiopoulos} et al., Adv. Discrete Math. Appl. 1, 91--106 (1998; Zbl 1088.37511)
Contopoulos, George; Voglis, Nikos Spectra of stretching numbers and helicity angles. (English) Zbl 1088.37509 Benest, Daniel (ed.) et al., Analysis and modelling of discrete dynamical systems. Reading: Gordon and Breach (ISBN 90-5699-625-8/hbk). Adv. Discrete Math. Appl. 1, 55-89 (1998). MSC: 37J10 37J40 65M99 PDFBibTeX XMLCite \textit{G. Contopoulos} and \textit{N. Voglis}, Adv. Discrete Math. Appl. 1, 55--89 (1998; Zbl 1088.37509)
Zou, Y.-K.; Beyn, W.-J. Invariant manifolds for nonautonomous systems with application to one-step methods. (English) Zbl 0908.34035 J. Dyn. Differ. Equations 10, No. 3, 379-407 (1998). MSC: 34C45 65L12 37J40 37B99 PDFBibTeX XMLCite \textit{Y. K. Zou} and \textit{W. J. Beyn}, J. Dyn. Differ. Equations 10, No. 3, 379--407 (1998; Zbl 0908.34035) Full Text: DOI
Tompaidis, Stathis Approximation of invariant surfaces by periodic orbits in high-dimensional maps: Some rigorous results. (English) Zbl 0867.58056 Exp. Math. 5, No. 3, 197-209 (1996). MSC: 37J40 37J99 65Y20 PDFBibTeX XMLCite \textit{S. Tompaidis}, Exp. Math. 5, No. 3, 197--209 (1996; Zbl 0867.58056) Full Text: DOI EuDML EMIS
Broer, H. W.; Osinga, H. M.; Vegter, G. Computing a normally hyperbolic invariant manifold of saddle type. (English) Zbl 0861.65068 Ladde, G. S. (ed.) et al., Dynamic systems and applications. Vol. 2. Proceedings of the 2nd international conference, Morehouse College, Atlanta, GA, USA, May 24–27, 1995. Atlanta, GA: Dynamic Publishers. 83-90 (1996). MSC: 65L99 37J40 57R30 PDFBibTeX XMLCite \textit{H. W. Broer} et al., in: Dynamic systems and applications. Vol. 2. Proceedings of the 2nd international conference, Morehouse College, Atlanta, GA, USA, May 24--27, 1995. Atlanta, GA: Dynamic Publishers. 83--90 (1996; Zbl 0861.65068)
Jones, Don A. On the behavior of attractors under finite difference approximation. (English) Zbl 0849.34037 Numer. Funct. Anal. Optimization 16, No. 9-10, 1155-1180 (1995). MSC: 34C40 34D45 37J40 34K99 35K55 65M06 PDFBibTeX XMLCite \textit{D. A. Jones}, Numer. Funct. Anal. Optim. 16, No. 9--10, 1155--1180 (1995; Zbl 0849.34037) Full Text: DOI
McLaughlin, David W.; Overman, Edward A. II Whiskered tori for integrable PDE’s: Chaotic behavior in near integrable PDE’s. (English) Zbl 0843.35116 Keller, Joseph B. (ed.) et al., Surveys in Applied Mathematics. Vol. 1. New York, NY: Plenum Press. 83-203 (1995). MSC: 35Q55 65Z05 37D45 37J40 PDFBibTeX XMLCite \textit{D. W. McLaughlin} and \textit{E. A. Overman II}, in: Surveys in Applied Mathematics. Vol. 1. New York, NY: Plenum Press. 83--203 (1995; Zbl 0843.35116)
Giorgilli, Antonio Energy equipartition and Nekhoroshev-type estimates for large systems. (English) Zbl 0833.65066 Dumas, H. S. (ed.) et al., Hamiltonian dynamical systems: history, theory, and applications. Proceedings of the international conference held at the University of Cincinnati, OH (USA), March 1992. New York, NY: Springer-Verlag. IMA Vol. Math. Appl. 63, 147-161 (1995). MSC: 65L05 37-XX PDFBibTeX XMLCite \textit{A. Giorgilli}, IMA Vol. Math. Appl. 63, 147--161 (1995; Zbl 0833.65066)
Ragos, O.; Zagouras, C. G. A numerical algorithm for the determination of regions of quasi-periodic motion in two-dimensional Hamiltonian systems. (English) Zbl 0881.65067 Bainov, Drumi (ed.) et al., Proceedings of the 3rd international colloquium on numerical analysis, Plovdiv, Bulgaria, August 13–17, 1994. Invited lectures and short communications. Singapore: SCT Publishing, 157-163 (1995). MSC: 65L05 37-XX 34C25 PDFBibTeX XMLCite \textit{O. Ragos} and \textit{C. G. Zagouras}, in: Proceedings of the 3rd international colloquium on numerical analysis, Plovdiv, Bulgaria, August 13--17, 1994. Invited lectures and short communications. Singapore: SCT Publishing. 157--163 (1995; Zbl 0881.65067)
Busvelle, E.; Kharab, R.; Maciejewski, A. J.; Strelcyn, J.-M. Numerical integration of differential equations in the presence of first integrals: Observer method. (English) Zbl 0819.34008 Appl. Math. 22, No. 3, 373-418 (1994). Reviewer: E.Hairer (Genève) MSC: 65J99 65L06 37J40 PDFBibTeX XMLCite \textit{E. Busvelle} et al., Appl. Math. 22, No. 3, 373--418 (1994; Zbl 0819.34008) Full Text: DOI EuDML
Garabedian, P. R. A unified theory of tokamaks and stellarators. (English) Zbl 0801.76098 Commun. Pure Appl. Math. 47, No. 3, 281-292 (1994). MSC: 76X05 76M25 65C05 PDFBibTeX XMLCite \textit{P. R. Garabedian}, Commun. Pure Appl. Math. 47, No. 3, 281--292 (1994; Zbl 0801.76098) Full Text: DOI
Sanz-Serna, J. M. Symplectic integrators for Hamiltonian problems: An overview. (English) Zbl 0762.65043 Acta Numerica 1992, 243-286 (1992). Reviewer: L.-I.Anita (Iaşi) MSC: 65L05 37J99 PDFBibTeX XMLCite \textit{J. M. Sanz-Serna}, Acta Numerica 1992, 243--286 (1992; Zbl 0762.65043)
Lowenstein, J. H. Interpolating Hamiltonians for a stochastic-web map with quasicrystalline symmetry. (English) Zbl 1055.37581 Chaos 2, No. 3, 413-422 (1992). MSC: 37J40 70H05 37J15 65P10 PDFBibTeX XMLCite \textit{J. H. Lowenstein}, Chaos 2, No. 3, 413--422 (1992; Zbl 1055.37581) Full Text: DOI
De la Llave, R.; Rana, D. Accurate strategies for K. A. M. bounds and their implementation. (English) Zbl 0747.65039 Computer aided proofs in analysis, Proc. IMA Participating Inst. Conf., Cincinnati/OH (USA), IMA Vol. Math. Appl. 28, 127-146 (1991). Reviewer: J.Albrycht (Poznań) MSC: 65J15 65G30 70K50 70F15 37J40 37C55 37C75 PDFBibTeX XMLCite \textit{R. De la Llave} and \textit{D. Rana}, IMA Vol. Math. Appl. 28, 127--146 (1991; Zbl 0747.65039)
Nipp, K. Numerical integration of stiff ODE’s of singular perturbation type. (English) Zbl 0747.65052 Z. Angew. Math. Phys. 42, No. 1, 53-79 (1991). Reviewer: J.B.Butler jun.(Portland) MSC: 65L05 65L70 92C20 37J40 34A34 34E13 34E15 PDFBibTeX XMLCite \textit{K. Nipp}, Z. Angew. Math. Phys. 42, No. 1, 53--79 (1991; Zbl 0747.65052) Full Text: DOI
De la Llave, R.; Rana, David Accurate strategies for small divisor problems. (English) Zbl 0739.58060 Bull. Am. Math. Soc., New Ser. 22, No. 1, 85-90 (1990). MSC: 37C55 70K50 37J40 65J15 30D05 37C75 PDFBibTeX XMLCite \textit{R. De la Llave} and \textit{D. Rana}, Bull. Am. Math. Soc., New Ser. 22, No. 1, 85--90 (1990; Zbl 0739.58060) Full Text: DOI
Vul, E. B. Some numerical studies of dynamical systems. (English) Zbl 0689.65050 Dynamical systems and ergodic theory, 28th Sem. St. Banach Int. Math. Cent., Warsaw/Pol. 1986, Banach Cent. Publ. 23, 351-354 (1989). Reviewer: F.Ling MSC: 65L05 65Q05 37D45 PDFBibTeX XML
Jupp, Alan H. The ideal resonance problem. A comparison of two formal solutions. III. (English) Zbl 0661.70030 Celestial Mech. 40, 87-93 (1987). MSC: 70K40 70K05 70H05 65L05 37J40 PDFBibTeX XMLCite \textit{A. H. Jupp}, Celest. Mech. 40, 87--93 (1987; Zbl 0661.70030) Full Text: DOI
Jupp, A. H.; Abdulla, A. Y. The ideal resonance problem. A comparison of two formal solutions. I. (English) Zbl 0596.70025 Celestial Mech. 34, 411-423 (1984). Reviewer: H.Rüßmann MSC: 70K40 70K05 65L05 37J40 70H05 PDFBibTeX XMLCite \textit{A. H. Jupp} and \textit{A. Y. Abdulla}, Celest. Mech. 34, 411--423 (1984; Zbl 0596.70025) Full Text: DOI