Martynchuk, N.; Broer, H. W.; Efstathiou, K. Recent advances in the monodromy theory of integrable Hamiltonian systems. (English) Zbl 07298852 Indag. Math., New Ser. 32, No. 1, 193-223 (2021). MSC: 37J30 37J35 81S08 81S10 81S05 PDF BibTeX XML Cite \textit{N. Martynchuk} et al., Indag. Math., New Ser. 32, No. 1, 193--223 (2021; Zbl 07298852) Full Text: DOI
Wu, Yuan; Yuan, Xiaoping On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range. (English) Zbl 1453.37071 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 202, Article ID 112120, 34 p. (2021). MSC: 37K55 37J40 70H08 70K43 PDF BibTeX XML Cite \textit{Y. Wu} and \textit{X. Yuan}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 202, Article ID 112120, 34 p. (2021; Zbl 1453.37071) Full Text: DOI
Markeev, A. P.; Chekhovskaya, T. N. On nonlinear oscillations and stability of coupled pendulums in the case of a multiple resonance. (English) Zbl 07319346 Nelineĭn. Din. 16, No. 4, 607-623 (2020). MSC: 70E55 70H09 70H14 PDF BibTeX XML Cite \textit{A. P. Markeev} and \textit{T. N. Chekhovskaya}, Nelineĭn. Din. 16, No. 4, 607--623 (2020; Zbl 07319346) Full Text: DOI MNR
Xie, Yuxin; Liu, Siming From period to quasiperiod to chaos: a continuous spectrum of orbits of charged particles trapped in a dipole magnetic field. (English) Zbl 1451.78017 Chaos 30, No. 12, 123108, 12 p. (2020). MSC: 78A35 37N20 37J46 37M05 PDF BibTeX XML Cite \textit{Y. Xie} and \textit{S. Liu}, Chaos 30, No. 12, 123108, 12 p. (2020; Zbl 1451.78017) Full Text: DOI
Walsh, James A window into the world of KAM theory. (English) Zbl 07279635 Math. Mag. 93, No. 4, 244-260 (2020). MSC: 37J40 PDF BibTeX XML Cite \textit{J. Walsh}, Math. Mag. 93, No. 4, 244--260 (2020; Zbl 07279635) Full Text: DOI
Bounemoura, Abed Positive measure of KAM tori for finitely differentiable Hamiltonians. (Mesure positive de tores invariants pour les systèmes hamiltoniens en différentiabilité finie.) (English. French summary) Zbl 07268823 J. Éc. Polytech., Math. 7, 1113-1132 (2020). MSC: 37J40 37C55 70K43 PDF BibTeX XML Cite \textit{A. Bounemoura}, J. Éc. Polytech., Math. 7, 1113--1132 (2020; Zbl 07268823) Full Text: DOI
Marò, Stefano Orbit determination for standard-like maps: asymptotic expansion of the confidence region in regular zones. (English) Zbl 1448.70068 Celest. Mech. Dyn. Astron. 132, No. 8, Paper No. 40, 18 p. (2020). MSC: 70M20 PDF BibTeX XML Cite \textit{S. Marò}, Celest. Mech. Dyn. Astron. 132, No. 8, Paper No. 40, 18 p. (2020; Zbl 1448.70068) Full Text: DOI
Cao, Zhenbang; Zhang, Xiaoming; Li, Denghui; Yin, Shan; Xie, Jianhua Existence of invariant curves for a Fermi-type impact absorber. (English) Zbl 1434.70045 Nonlinear Dyn. 99, No. 4, 2647-2656 (2020). MSC: 70H33 34C14 PDF BibTeX XML Cite \textit{Z. Cao} et al., Nonlinear Dyn. 99, No. 4, 2647--2656 (2020; Zbl 1434.70045) Full Text: DOI
Martynchuk, N.; Broer, H. W.; Efstathiou, K. Hamiltonian monodromy and Morse theory. (English) Zbl 07191225 Commun. Math. Phys. 375, No. 2, 1373-1392 (2020). MSC: 37J35 37J99 37J05 37J15 70H05 PDF BibTeX XML Cite \textit{N. Martynchuk} et al., Commun. Math. Phys. 375, No. 2, 1373--1392 (2020; Zbl 07191225) Full Text: DOI
Lim, Chjan C. General Jacobi coordinates and Herman resonance for some nonheliocentric celestial \(N\)-body problems. (English) Zbl 07189261 Regul. Chaotic Dyn. 25, No. 2, 149-165 (2020). MSC: 70 37J40 PDF BibTeX XML Cite \textit{C. C. Lim}, Regul. Chaotic Dyn. 25, No. 2, 149--165 (2020; Zbl 07189261) Full Text: DOI
Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael Existence of whiskered KAM tori of conformally symplectic systems. (English) Zbl 07141430 Nonlinearity 33, No. 1, 538-597 (2020). MSC: 70K43 70K20 34D35 PDF BibTeX XML Cite \textit{R. C. Calleja} et al., Nonlinearity 33, No. 1, 538--597 (2020; Zbl 07141430) Full Text: DOI
Chierchia, L.; Koudjinan, C. E. V. I. Arnold’s “Pointwise” KAM theorem. (English) Zbl 1435.37085 Regul. Chaotic Dyn. 24, No. 6, 583-606 (2019). MSC: 37J40 37J06 37J25 70H08 PDF BibTeX XML Cite \textit{L. Chierchia} and \textit{C. E. Koudjinan}, Regul. Chaotic Dyn. 24, No. 6, 583--606 (2019; Zbl 1435.37085) Full Text: DOI
Bouthelja, Moudhaffar KAM for the nonlinear wave equation on the circle: a normal form theorem. (English) Zbl 1441.37083 Boll. Unione Mat. Ital. 12, No. 3, 363-424 (2019). MSC: 37K55 35L05 35L70 PDF BibTeX XML Cite \textit{M. Bouthelja}, Boll. Unione Mat. Ital. 12, No. 3, 363--424 (2019; Zbl 1441.37083) Full Text: DOI arXiv
Wang, Kaizhi; Wang, Lin; Yan, Jun Aubry-Mather theory for contact Hamiltonian systems. (English) Zbl 1429.37034 Commun. Math. Phys. 366, No. 3, 981-1023 (2019). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37J55 37J51 37J40 70G45 PDF BibTeX XML Cite \textit{K. Wang} et al., Commun. Math. Phys. 366, No. 3, 981--1023 (2019; Zbl 1429.37034) Full Text: DOI
Luo, Tong; Xu, Ming Dynamics of the spatial restricted three-body problem stabilized by Hamiltonian structure-preserving control. (English) Zbl 1422.93055 Nonlinear Dyn. 94, No. 3, 1889-1905 (2018). MSC: 93B18 70Q05 70H33 PDF BibTeX XML Cite \textit{T. Luo} and \textit{M. Xu}, Nonlinear Dyn. 94, No. 3, 1889--1905 (2018; Zbl 1422.93055) Full Text: DOI
Li, Hepeng The almost-periodic solutions of the weakly coupled pendulum equations. (English) Zbl 1446.70038 Adv. Difference Equ. 2018, Paper No. 157, 22 p. (2018). MSC: 70H12 34C15 37J40 70H08 PDF BibTeX XML Cite \textit{H. Li}, Adv. Difference Equ. 2018, Paper No. 157, 22 p. (2018; Zbl 1446.70038) Full Text: DOI
Villanueva, Jordi A parameterization method for Lagrangian tori of exact symplectic maps of \(\mathbb{R}^{2r}\). (English) Zbl 1408.37093 SIAM J. Appl. Dyn. Syst. 17, No. 3, 2289-2331 (2018). MSC: 37J10 37J40 70K43 PDF BibTeX XML Cite \textit{J. Villanueva}, SIAM J. Appl. Dyn. Syst. 17, No. 3, 2289--2331 (2018; Zbl 1408.37093) Full Text: DOI
Volpi, Mara; Locatelli, Ugo; Sansottera, Marco A reverse KAM method to estimate unknown mutual inclinations in exoplanetary systems. (English) Zbl 1391.70034 Celest. Mech. Dyn. Astron. 130, No. 5, Paper No. 36, 17 p. (2018). MSC: 70F10 70G60 70F15 37N05 PDF BibTeX XML Cite \textit{M. Volpi} et al., Celest. Mech. Dyn. Astron. 130, No. 5, Paper No. 36, 17 p. (2018; Zbl 1391.70034) Full Text: DOI
Pinzari, Gabriella On the co-existence of maximal and whiskered tori in the planetary three-body problem. (English) Zbl 1391.70024 J. Math. Phys. 59, No. 5, 052701, 37 p. (2018). MSC: 70F07 70F15 70E50 PDF BibTeX XML Cite \textit{G. Pinzari}, J. Math. Phys. 59, No. 5, 052701, 37 p. (2018; Zbl 1391.70024) Full Text: DOI
Chen, Dong Positive metric entropy in nondegenerate nearly integrable systems. (English) Zbl 1402.37071 J. Mod. Dyn. 11, 43-56 (2017). MSC: 37J40 37A35 53C60 70H08 PDF BibTeX XML Cite \textit{D. Chen}, J. Mod. Dyn. 11, 43--56 (2017; Zbl 1402.37071) Full Text: DOI
Giorgilli, Antonio; Locatelli, Ugo; Sansottera, Marco Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability in the light of Kolmogorov and Nekhoroshev theories. (English) Zbl 1390.70020 Regul. Chaotic Dyn. 22, No. 1, 54-77 (2017). MSC: 70F10 37J40 37N05 70-08 70H08 PDF BibTeX XML Cite \textit{A. Giorgilli} et al., Regul. Chaotic Dyn. 22, No. 1, 54--77 (2017; Zbl 1390.70020) Full Text: DOI
Villanueva, Jordi A new approach to the parameterization method for Lagrangian tori of Hamiltonian systems. (English) Zbl 1456.37067 J. Nonlinear Sci. 27, No. 2, 495-530 (2017). MSC: 37J40 70K43 70H08 PDF BibTeX XML Cite \textit{J. Villanueva}, J. Nonlinear Sci. 27, No. 2, 495--530 (2017; Zbl 1456.37067) Full Text: DOI
Bounemoura, Abed Generic perturbations of linear integrable Hamiltonian systems. (English) Zbl 1368.37069 Regul. Chaotic Dyn. 21, No. 6, 665-681 (2016). MSC: 37J40 37J25 PDF BibTeX XML Cite \textit{A. Bounemoura}, Regul. Chaotic Dyn. 21, No. 6, 665--681 (2016; Zbl 1368.37069) Full Text: DOI arXiv
Janković, Marija R.; Dmitrašinović, V. Angular momentum and topological dependence of Kepler’s third law in the Broucke-Hadjidemetriou-Hénon family of periodic three-body orbits. (English) Zbl 1356.70014 Phys. Rev. Lett. 116, No. 6, Article ID 064301, 5 p. (2016). MSC: 70F07 70K20 70K42 70K43 70K50 PDF BibTeX XML Cite \textit{M. R. Janković} and \textit{V. Dmitrašinović}, Phys. Rev. Lett. 116, No. 6, Article ID 064301, 5 p. (2016; Zbl 1356.70014) Full Text: DOI
Gomes, Diogo; Nurbekyan, Levon An infinite-dimensional weak KAM theory via random variables. (English) Zbl 1352.37174 Discrete Contin. Dyn. Syst. 36, No. 11, 6167-6185 (2016). MSC: 37K05 37K55 49L20 49L25 35F21 PDF BibTeX XML Cite \textit{D. Gomes} and \textit{L. Nurbekyan}, Discrete Contin. Dyn. Syst. 36, No. 11, 6167--6185 (2016; Zbl 1352.37174) Full Text: DOI arXiv
Solanpää, J.; Luukko, P. J. J.; Räsänen, E. Bill2d – a software package for classical two-dimensional Hamiltonian systems. (English) Zbl 1344.37004 Comput. Phys. Commun. 199, 133-138 (2016). MSC: 37-04 70-04 37D50 PDF BibTeX XML Cite \textit{J. Solanpää} et al., Comput. Phys. Commun. 199, 133--138 (2016; Zbl 1344.37004) Full Text: DOI
Xu, Junxiang; Lu, Xuezhu General KAM theorems and their applications to invariant tori with prescribed frequencies. (English) Zbl 1344.37070 Regul. Chaotic Dyn. 21, No. 1, 107-125 (2016). MSC: 37J40 34C27 70H08 PDF BibTeX XML Cite \textit{J. Xu} and \textit{X. Lu}, Regul. Chaotic Dyn. 21, No. 1, 107--125 (2016; Zbl 1344.37070) Full Text: DOI arXiv
Delshams, Amadeu; de la Llave, Rafael; Seara, Tere M. Instability of high dimensional Hamiltonian systems: multiple resonances do not impede diffusion. (English) Zbl 1355.37074 Adv. Math. 294, 689-755 (2016). MSC: 37J25 37J40 PDF BibTeX XML Cite \textit{A. Delshams} et al., Adv. Math. 294, 689--755 (2016; Zbl 1355.37074) Full Text: DOI arXiv
Cong, Fuzhong; Hong, Jialin; Li, Hongtian Quasi-effective stability for nearly integrable Hamiltonian systems. (English) Zbl 1360.37144 Discrete Contin. Dyn. Syst., Ser. B 21, No. 1, 67-80 (2016). MSC: 37J25 37J40 70H08 PDF BibTeX XML Cite \textit{F. Cong} et al., Discrete Contin. Dyn. Syst., Ser. B 21, No. 1, 67--80 (2016; Zbl 1360.37144) Full Text: DOI
Cong, Fuzhong; Li, Hongtian Quasi-effective stability for a nearly integrable volume-preserving mapping. (English) Zbl 1333.37085 Discrete Contin. Dyn. Syst., Ser. B 20, No. 7, 1959-1970 (2015). MSC: 37J40 37E40 37J25 PDF BibTeX XML Cite \textit{F. Cong} and \textit{H. Li}, Discrete Contin. Dyn. Syst., Ser. B 20, No. 7, 1959--1970 (2015; Zbl 1333.37085) Full Text: DOI
Hanßmann, Heinz Perturbations of superintegrable systems. (English) Zbl 1314.37045 Acta Appl. Math. 137, No. 1, 79-95 (2015). MSC: 37J40 PDF BibTeX XML Cite \textit{H. Hanßmann}, Acta Appl. Math. 137, No. 1, 79--95 (2015; Zbl 1314.37045) Full Text: DOI
Jong, Wu Hwan; Paek, Jin Chol Existence of invariant tori for differentiable Hamiltonian vector fields without action-angle variables. (English) Zbl 1354.37072 Chaos Solitons Fractals 68, 114-122 (2014). MSC: 37K40 PDF BibTeX XML Cite \textit{W. H. Jong} and \textit{J. C. Paek}, Chaos Solitons Fractals 68, 114--122 (2014; Zbl 1354.37072) Full Text: DOI arXiv
Fortunati, Alessandro; Wiggins, Stephen Persistence of Diophantine flows for quadratic nearly integrable Hamiltonians under slowly decaying aperiodic time dependence. (English) Zbl 1308.70029 Regul. Chaotic Dyn. 19, No. 5, 586-600 (2014). MSC: 70H08 37J40 37J25 PDF BibTeX XML Cite \textit{A. Fortunati} and \textit{S. Wiggins}, Regul. Chaotic Dyn. 19, No. 5, 586--600 (2014; Zbl 1308.70029) Full Text: DOI arXiv
Fortunati, Alessandro; Wiggins, Stephen Normal form and Nekhoroshev stability for nearly integrable Hamiltonian systems with unconditionally slow aperiodic time dependence. (English) Zbl 1309.70026 Regul. Chaotic Dyn. 19, No. 3, 363-373 (2014). MSC: 70H08 37J25 37J40 PDF BibTeX XML Cite \textit{A. Fortunati} and \textit{S. Wiggins}, Regul. Chaotic Dyn. 19, No. 3, 363--373 (2014; Zbl 1309.70026) Full Text: DOI arXiv
Bounemoura, Abed; Fischler, Stéphane The classical KAM theorem for Hamiltonian systems via rational approximations. (English) Zbl 1339.37042 Regul. Chaotic Dyn. 19, No. 2, 251-265 (2014). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 37J25 37J40 70H08 70H09 PDF BibTeX XML Cite \textit{A. Bounemoura} and \textit{S. Fischler}, Regul. Chaotic Dyn. 19, No. 2, 251--265 (2014; Zbl 1339.37042) Full Text: DOI arXiv
Lu, Xuezhu; Xu, Junxiang Invariant tori with prescribed frequency for nearly integrable Hamiltonian systems. (English) Zbl 1345.70027 J. Math. Phys. 55, No. 8, 082702, 12 p. (2014). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 70H08 PDF BibTeX XML Cite \textit{X. Lu} and \textit{J. Xu}, J. Math. Phys. 55, No. 8, 082702, 12 p. (2014; Zbl 1345.70027) Full Text: DOI
Gorban, Alexander N.; Karlin, Ilya Hilbert’s 6th problem: exact and approximate hydrodynamic manifolds for kinetic equations. (English) Zbl 1294.35052 Bull. Am. Math. Soc., New Ser. 51, No. 2, 187-246 (2014). MSC: 35Q20 35Q35 76P05 82B40 35C20 82C40 PDF BibTeX XML Cite \textit{A. N. Gorban} and \textit{I. Karlin}, Bull. Am. Math. Soc., New Ser. 51, No. 2, 187--246 (2014; Zbl 1294.35052) Full Text: DOI arXiv
Bernardi, Olga; Cardin, Franco; Guzzo, Massimiliano Convergence to the time average by stochastic regularization. (English) Zbl 1420.37045 J. Nonlinear Math. Phys. 20, No. 1, 9-27 (2013). MSC: 37J40 37H10 37A30 PDF BibTeX XML Cite \textit{O. Bernardi} et al., J. Nonlinear Math. Phys. 20, No. 1, 9--27 (2013; Zbl 1420.37045) Full Text: DOI
Guzzo, Massimiliano; Lega, Elena The numerical detection of the Arnold web and its use for long-term diffusion studies in conservative and weakly dissipative systems. (English) Zbl 1331.37082 Chaos 23, No. 2, 023124, 12 p. (2013). MSC: 37J40 37M99 37J25 37J15 PDF BibTeX XML Cite \textit{M. Guzzo} and \textit{E. Lega}, Chaos 23, No. 2, 023124, 12 p. (2013; Zbl 1331.37082) Full Text: DOI
Calleja, Renato C.; Celletti, Alessandra; de la Llave, Rafael A KAM theory for conformally symplectic systems: efficient algorithms and their validation. (English) Zbl 1345.37078 J. Differ. Equations 255, No. 5, 978-1049 (2013). MSC: 37K55 37L99 70K43 70K20 PDF BibTeX XML Cite \textit{R. C. Calleja} et al., J. Differ. Equations 255, No. 5, 978--1049 (2013; Zbl 1345.37078) Full Text: DOI
Bernardi, Olga; Cardin, Franco; Guzzo, Massimiliano New estimates for Evans’ variational approach to weak KAM theory. (English) Zbl 1277.35127 Commun. Contemp. Math. 15, No. 2, Paper No. 1250055, 36 p. (2013). Reviewer: Jiansheng Geng (Nanjing) MSC: 35F21 70H20 70H08 70H30 PDF BibTeX XML Cite \textit{O. Bernardi} et al., Commun. Contemp. Math. 15, No. 2, Paper No. 1250055, 36 p. (2013; Zbl 1277.35127) Full Text: DOI arXiv
Wu, Yun Chao; Wang, Yi Qian The stability of the elliptic equilibrium of planar quasi-periodic Hamiltonian systems. (English) Zbl 1334.37057 Acta Math. Sin., Engl. Ser. 28, No. 4, 801-816 (2012). MSC: 37J25 34D20 PDF BibTeX XML Cite \textit{Y. C. Wu} and \textit{Y. Q. Wang}, Acta Math. Sin., Engl. Ser. 28, No. 4, 801--816 (2012; Zbl 1334.37057) Full Text: DOI
Balasuriya, Sanjeeva Explicit invariant manifolds and specialised trajectories in a class of unsteady flows. (English) Zbl 1309.76044 Phys. Fluids 24, No. 12, Paper No. 127101, 27 p. (2012). MSC: 76B47 37J40 35Q35 PDF BibTeX XML Cite \textit{S. Balasuriya}, Phys. Fluids 24, No. 12, Paper No. 127101, 27 p. (2012; Zbl 1309.76044) Full Text: DOI
Vaidya, Umesh; Mezić, Igor Existence of invariant tori in three dimensional maps with degeneracy. (English) Zbl 1261.70006 Physica D 241, No. 13, 1136-1145 (2012). Reviewer: Ahgel Zhivkov (Sofia) MSC: 70H08 37J40 PDF BibTeX XML Cite \textit{U. Vaidya} and \textit{I. Mezić}, Physica D 241, No. 13, 1136--1145 (2012; Zbl 1261.70006) Full Text: DOI arXiv
Li, Xuemei; Yuan, Xiaoping Quasi-periodic solutions for perturbed autonomous delay differential equations. (English) Zbl 1244.34093 J. Differ. Equations 252, No. 6, 3752-3796 (2012). Reviewer: Gheorghe Moroşanu (Budapest) MSC: 34K14 34K27 PDF BibTeX XML Cite \textit{X. Li} and \textit{X. Yuan}, J. Differ. Equations 252, No. 6, 3752--3796 (2012; Zbl 1244.34093) Full Text: DOI
Guzzo, Massimiliano; Lega, Elena; Froeschlé, Claude First numerical investigation of a conjecture by N. N. Nekhoroshev about stability in quasi-integrable systems. (English) Zbl 1317.37059 Chaos 21, No. 3, 033101, 12 p. (2011). MSC: 37J40 37J25 70H08 70H14 PDF BibTeX XML Cite \textit{M. Guzzo} et al., Chaos 21, No. 3, 033101, 12 p. (2011; Zbl 1317.37059) Full Text: DOI
Arnaud, Marie-Claude The link between the shape of the irrational Aubry-Mather sets and their Lyapunov exponents. (English) Zbl 1257.37028 Ann. Math. (2) 174, No. 3, 1571-1601 (2011). Reviewer: Božidar Jovanović (Beograd) MSC: 37E40 37J50 PDF BibTeX XML Cite \textit{M.-C. Arnaud}, Ann. Math. (2) 174, No. 3, 1571--1601 (2011; Zbl 1257.37028) Full Text: DOI arXiv
Hanßmann, Heinz Non-degeneracy conditions in KAM theory. (English) Zbl 1253.37058 Indag. Math., New Ser. 22, No. 3-4, 241-256 (2011). MSC: 37J40 PDF BibTeX XML Cite \textit{H. Hanßmann}, Indag. Math., New Ser. 22, No. 3--4, 241--256 (2011; Zbl 1253.37058) Full Text: DOI
Katsanikas, M.; Patsis, P. A. The structure of invariant tori in a 3D galactic potential. (English) Zbl 1210.85003 Int. J. Bifurcation Chaos Appl. Sci. Eng. 21, No. 2, 467-496 (2011). MSC: 85A05 37J40 34C45 37J45 PDF BibTeX XML Cite \textit{M. Katsanikas} and \textit{P. A. Patsis}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 21, No. 2, 467--496 (2011; Zbl 1210.85003) Full Text: DOI arXiv
Cheng, Chong Qing Non-existence of KAM torus. (English) Zbl 1209.37065 Acta Math. Sin., Engl. Ser. 27, No. 2, 397-404 (2011). MSC: 37J40 37J50 70H08 PDF BibTeX XML Cite \textit{C. Q. Cheng}, Acta Math. Sin., Engl. Ser. 27, No. 2, 397--404 (2011; Zbl 1209.37065) Full Text: DOI
Stenlund, Mikko An expansion of the homoclinic splitting matrix for the rapidly, quasiperiodically, forced pendulum. (English) Zbl 1311.70024 J. Math. Phys. 51, No. 7, 072902, 40 p. (2010). MSC: 70F20 70H05 34C37 PDF BibTeX XML Cite \textit{M. Stenlund}, J. Math. Phys. 51, No. 7, 072902, 40 p. (2010; Zbl 1311.70024) Full Text: DOI arXiv
dos Santos, F.; Mansilla, José E.; Vidal, C. Stability of equilibrium solutions of autonomous and periodic Hamiltonian systems with \(n\)-degrees of freedom in the case of single resonance. (English) Zbl 1209.37026 J. Dyn. Differ. Equations 22, No. 4, 805-821 (2010). Reviewer: Vladimir Răsvan (Craiova) MSC: 37C75 34D20 34A25 PDF BibTeX XML Cite \textit{F. dos Santos} et al., J. Dyn. Differ. Equations 22, No. 4, 805--821 (2010; Zbl 1209.37026) Full Text: DOI
Soga, Kohei A point-wise criterion for quasi-periodic motions in the KAM theory. (English) Zbl 1380.70042 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 10, 3151-3161 (2010). MSC: 70H08 37J40 70K43 34A12 34C25 PDF BibTeX XML Cite \textit{K. Soga}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 10, 3151--3161 (2010; Zbl 1380.70042) Full Text: DOI
Barwicz, Weronika; Ẓołądek, Henryk The restricted three body problem revisited. (English) Zbl 1379.70037 J. Math. Anal. Appl. 366, No. 2, 663-672 (2010). MSC: 70F07 37J05 37N05 PDF BibTeX XML Cite \textit{W. Barwicz} and \textit{H. Ẓołądek}, J. Math. Anal. Appl. 366, No. 2, 663--672 (2010; Zbl 1379.70037) Full Text: DOI
Maier, R.; Soares, I. Damião; Tonini, E. V. Bouncing braneworld cosmologies and initial conditions to inflation. (English) Zbl 1222.83174 Phys. Rev. D (3) 79, No. 2, Article ID 023522, 19 p. (2009). MSC: 83E15 83F05 PDF BibTeX XML Cite \textit{R. Maier} et al., Phys. Rev. D (3) 79, No. 2, Article ID 023522, 19 p. (2009; Zbl 1222.83174) Full Text: DOI
Frasca, Marco Dual Lindstedt series and Kolmogorov-Arnol’d-Moser theorem. (English) Zbl 1236.37034 J. Math. Phys. 50, No. 10, 102904, 8 p. (2009). MSC: 37J40 34E13 70H05 PDF BibTeX XML Cite \textit{M. Frasca}, J. Math. Phys. 50, No. 10, 102904, 8 p. (2009; Zbl 1236.37034) Full Text: DOI arXiv
Fontich, Ernest; de la Llave, Rafael; Sire, Yannick Construction of invariant whiskered tori by a parameterization method. I: Maps and flows in finite dimensions. (English) Zbl 1209.37066 J. Differ. Equations 246, No. 8, 3136-3213 (2009). Reviewer: Maria Saprykina (Stockholm) MSC: 37J40 37D05 70H08 70K43 PDF BibTeX XML Cite \textit{E. Fontich} et al., J. Differ. Equations 246, No. 8, 3136--3213 (2009; Zbl 1209.37066) Full Text: DOI arXiv
De Oliveira, H. P.; Soares, I. Damião; Tonini, E. V. Nonlinear resonance in the very early universe: sounds of the primordial music. (English) Zbl 1172.83348 Int. J. Mod. Phys. D 17, No. 13-14, 2459-2465 (2008). MSC: 83F05 37N20 PDF BibTeX XML Cite \textit{H. P. De Oliveira} et al., Int. J. Mod. Phys. D 17, No. 13--14, 2459--2465 (2008; Zbl 1172.83348) Full Text: DOI
Zhang, Dongfeng; Xu, Junxiang Invariant hyperbolic tori for Gevrey-smooth Hamiltonian systems under Rüssmann’s non-degeneracy condition. (English) Zbl 1148.70010 Acta Math. Sin., Engl. Ser. 24, No. 10, 1625-1636 (2008). MSC: 70H08 70H09 37N05 PDF BibTeX XML Cite \textit{D. Zhang} and \textit{J. Xu}, Acta Math. Sin., Engl. Ser. 24, No. 10, 1625--1636 (2008; Zbl 1148.70010) Full Text: DOI
Villanueva, Jordi Kolmogorov theorem revisited. (English) Zbl 1143.37044 J. Differ. Equations 244, No. 9, 2251-2276 (2008). Reviewer: Constantin Udrişte (Bucureşti) MSC: 37J40 PDF BibTeX XML Cite \textit{J. Villanueva}, J. Differ. Equations 244, No. 9, 2251--2276 (2008; Zbl 1143.37044) Full Text: DOI
Zhang, Li; Xu, Junxiang Persistence of invariant torus in Hamiltonian systems with two-degree of freedom. (English) Zbl 1134.37025 J. Math. Anal. Appl. 338, No. 2, 793-802 (2008). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 37J40 70H08 PDF BibTeX XML Cite \textit{L. Zhang} and \textit{J. Xu}, J. Math. Anal. Appl. 338, No. 2, 793--802 (2008; Zbl 1134.37025) Full Text: DOI
Zhu, Wenzhuang; Liu, Baifeng; Liu, Zhenxin The hyperbolic invariant tori of symplectic mappings. (English) Zbl 1123.37026 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 1, 109-126 (2008). MSC: 37J40 37J10 37E40 PDF BibTeX XML Cite \textit{W. Zhu} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 1, 109--126 (2008; Zbl 1123.37026) Full Text: DOI
Guzzo, Massimiliano; Bernardi, Olga; Cardin, Franco The experimental localization of Aubry-Mather sets using regularization techniques inspired by viscosity theory. (English) Zbl 1163.37330 Chaos 17, No. 3, 033107, 9 p. (2007). MSC: 37D45 PDF BibTeX XML Cite \textit{M. Guzzo} et al., Chaos 17, No. 3, 033107, 9 p. (2007; Zbl 1163.37330) Full Text: DOI arXiv
Stenlund, Mikko Construction of whiskers for the quasiperiodically forced pendulum. (English) Zbl 1142.70011 Rev. Math. Phys. 19, No. 8, 823-877 (2007). MSC: 70K40 70K43 70H09 37N05 PDF BibTeX XML Cite \textit{M. Stenlund}, Rev. Math. Phys. 19, No. 8, 823--877 (2007; Zbl 1142.70011) Full Text: DOI arXiv
de Simone, Emiliano A renormalization proof of the KAM theorem for non analytic perturbations. (English) Zbl 1148.37033 Rev. Math. Phys. 19, No. 6, 639-675 (2007). MSC: 37J40 82B28 PDF BibTeX XML Cite \textit{E. de Simone}, Rev. Math. Phys. 19, No. 6, 639--675 (2007; Zbl 1148.37033) Full Text: DOI arXiv
Chen, Shun Qing; Yuan, Xiao Ping A KAM theorem for reversible systems of infinite dimension. (English) Zbl 1129.37043 Acta Math. Sin., Engl. Ser. 23, No. 10, 1777-1796 (2007). MSC: 37K55 34C15 34C27 PDF BibTeX XML Cite \textit{S. Q. Chen} and \textit{X. P. Yuan}, Acta Math. Sin., Engl. Ser. 23, No. 10, 1777--1796 (2007; Zbl 1129.37043) Full Text: DOI
Roy, Nicolas A semi-classical K.A.M. theorem. (English) Zbl 1117.81066 Commun. Partial Differ. Equations 32, No. 5, 745-770 (2007). MSC: 81Q20 37J40 PDF BibTeX XML Cite \textit{N. Roy}, Commun. Partial Differ. Equations 32, No. 5, 745--770 (2007; Zbl 1117.81066) Full Text: DOI arXiv
Lansel, Steven; Porter, Mason A.; Bunimovich, Leonid A. One-particle and few-particle billiards. (English) Zbl 1144.37365 Chaos 16, No. 1, 013129, 12 p. (2006). MSC: 37D45 PDF BibTeX XML Cite \textit{S. Lansel} et al., Chaos 16, No. 1, 013129, 12 p. (2006; Zbl 1144.37365) Full Text: DOI arXiv
Froeschlé, Claude; Lega, Elena; Guzzo, Massimiliano Analysis of the chaotic behaviour of orbits diffusing along the Arnold web. (English) Zbl 1185.37141 Celest. Mech. Dyn. Astron. 95, No. 1-4, 141-153 (2006). MSC: 37J40 70H09 70K43 PDF BibTeX XML Cite \textit{C. Froeschlé} et al., Celest. Mech. Dyn. Astron. 95, No. 1--4, 141--153 (2006; Zbl 1185.37141) Full Text: DOI
Liu, Baifeng; Zhu, Wenzhuang; Han, Yuecai Persistence of lower-dimensional hyperbolic invariant tori for generalized Hamiltonian systems. (English) Zbl 1099.37046 J. Math. Anal. Appl. 322, No. 1, 251-275 (2006). MSC: 37J40 70H09 37D10 PDF BibTeX XML Cite \textit{B. Liu} et al., J. Math. Anal. Appl. 322, No. 1, 251--275 (2006; Zbl 1099.37046) Full Text: DOI
Delshams, Amadeu; de La Llave, Rafael; Seara, Tere M. Orbits of unbounded energy in quasi-periodic perturbations of geodesic flows. (English) Zbl 1091.37018 Adv. Math. 202, No. 1, 64-188 (2006). Reviewer: Mircea Puta (Timişoara) MSC: 37J40 37D40 37J45 37J25 53D25 70H08 PDF BibTeX XML Cite \textit{A. Delshams} et al., Adv. Math. 202, No. 1, 64--188 (2006; Zbl 1091.37018) Full Text: DOI
Mancini, Gianni; Srikanth, P. N. On periodic motions of a two dimensional Toda type chain. (English) Zbl 1096.37049 ESAIM, Control Optim. Calc. Var. 11, 72-87 (2005). Reviewer: Jens Rademacher (Berlin) MSC: 37K10 37K60 37J45 35Q53 58E30 47J30 PDF BibTeX XML Cite \textit{G. Mancini} and \textit{P. N. Srikanth}, ESAIM, Control Optim. Calc. Var. 11, 72--87 (2005; Zbl 1096.37049) Full Text: DOI Numdam EuDML
Liu, Zhenxin Persistence of lower dimensional invariant tori on sub-manifolds in Hamiltonian systems. (English) Zbl 1079.37051 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 61, No. 8, 1319-1342 (2005). Reviewer: Messoud A. Efendiev (Berlin) MSC: 37J15 37J40 PDF BibTeX XML Cite \textit{Z. Liu}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 61, No. 8, 1319--1342 (2005; Zbl 1079.37051) Full Text: DOI arXiv
Broer, H. W.; Hoveijn, I.; van Noort, M.; Simó, C.; Vegter, G. The parametrically forced pendulum: A case study in \(1\frac12\) degree of freedom. (English) Zbl 1061.37039 J. Dyn. Differ. Equations 16, No. 4, 897-947 (2004). Reviewer: Irina V. Konopleva (Ul’yanovsk) MSC: 37J20 37J40 37M20 70H08 PDF BibTeX XML Cite \textit{H. W. Broer} et al., J. Dyn. Differ. Equations 16, No. 4, 897--947 (2004; Zbl 1061.37039) Full Text: DOI
Yang, Ren Zi; Xu, Jun Xiang Effective reducibility of a class of linear differential equations with quasiperiodic coefficients. (English) Zbl 1069.34058 Acta Math. Sin., Engl. Ser. 20, No. 3, 525-532 (2004). Reviewer: S. D. Bajpai (Indore) MSC: 34C20 34D20 34A30 PDF BibTeX XML Cite \textit{R. Z. Yang} and \textit{J. X. Xu}, Acta Math. Sin., Engl. Ser. 20, No. 3, 525--532 (2004; Zbl 1069.34058) Full Text: DOI
Lodge, G.; Walsh, J. A.; Kramer, M. A trilinear three-body problem. (English) Zbl 1103.70006 Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 8, 2141-2155 (2003). Reviewer: Alexei Tsygvintsev (Lyon) MSC: 70F07 70H08 37N05 PDF BibTeX XML Cite \textit{G. Lodge} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 13, No. 8, 2141--2155 (2003; Zbl 1103.70006) Full Text: DOI
Haro, Àlex An algorithm to generate canonical transformations: Application to normal forms. (English) Zbl 1027.70025 Physica D 167, No. 3-4, 197-217 (2002). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 70H15 70-08 PDF BibTeX XML Cite \textit{À. Haro}, Physica D 167, No. 3--4, 197--217 (2002; Zbl 1027.70025) Full Text: DOI
Chandre, C.; Jauslin, H. R. Renormalization-group analysis for the transition to chaos in Hamiltonian systems. (English) Zbl 0994.70013 Phys. Rep. 365, No. 1, 1-64 (2002). MSC: 70H14 70H15 37N05 PDF BibTeX XML Cite \textit{C. Chandre} and \textit{H. R. Jauslin}, Phys. Rep. 365, No. 1, 1--64 (2002; Zbl 0994.70013) Full Text: DOI
Litvak-Hinenzon, Anna; Rom-Kedar, Vered Parabolic resonances in 3 degree of freedom near-integrable Hamiltonian systems. (English) Zbl 1036.70010 Physica D 164, No. 3-4, 213-250 (2002). Reviewer: Alexei Tsygvintsev (Lyon) MSC: 70H08 70K55 PDF BibTeX XML Cite \textit{A. Litvak-Hinenzon} and \textit{V. Rom-Kedar}, Physica D 164, No. 3--4, 213--250 (2002; Zbl 1036.70010) Full Text: DOI
Andreu, Miquel Angel; Celletti, Alessandra; Falcolini, Corrado Breakdown of librational invariant surfaces. (English) Zbl 1089.70511 Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 5, 975-982 (1999). MSC: 70F15 70K20 37N05 PDF BibTeX XML Cite \textit{M. A. Andreu} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 5, 975--982 (1999; Zbl 1089.70511) Full Text: DOI
Cong, Fuzhong; Li, Yong; Jin, Dejun Invariant hyperbolic tori for Hamiltonian systems with Rüssmann nondegeneracy conditions. (English) Zbl 0973.37036 Rocky Mt. J. Math. 29, No. 3, 831-851 (1999). Reviewer: Lev Lerman (Nizhny Novgorod) MSC: 37J40 PDF BibTeX XML Cite \textit{F. Cong} et al., Rocky Mt. J. Math. 29, No. 3, 831--851 (1999; Zbl 0973.37036) Full Text: DOI Link
Duclos, P.; Šťovíček, P.; Vittot, M. Perturbation of an eigenvalue from a dense point spectrum: a general Floquet Hamiltonian. (English) Zbl 0972.81041 Ann. Inst. Henri Poincaré, Phys. Théor. 71, No. 3, 241-301 (1999). Reviewer: Michael Perelmuter (Kyïv) MSC: 81Q15 81Q10 47E05 34L05 47N50 PDF BibTeX XML Cite \textit{P. Duclos} et al., Ann. Inst. Henri Poincaré, Phys. Théor. 71, No. 3, 241--301 (1999; Zbl 0972.81041) Full Text: Numdam EuDML
Ortega, Juan-Pablo; Ratiu, Tudor S. A Dirichlet criterion for the stability of periodic and relative periodic orbits in Hamiltonian systems. (English) Zbl 0977.34051 J. Geom. Phys. 32, No. 2, 131-159 (1999). Reviewer: Sergei Georgievich Zhuravlev (Moskva) MSC: 34D35 34C25 37D35 37J25 70H14 70H05 PDF BibTeX XML Cite \textit{J.-P. Ortega} and \textit{T. S. Ratiu}, J. Geom. Phys. 32, No. 2, 131--159 (1999; Zbl 0977.34051) Full Text: DOI
Sevryuk, M. B. The finite-dimensional reversible KAM theory. (English) Zbl 1194.37151 Physica D 112, No. 1-2, 132-147 (1998). MSC: 37N05 34C27 70H05 PDF BibTeX XML Cite \textit{M. B. Sevryuk}, Physica D 112, No. 1--2, 132--147 (1998; Zbl 1194.37151) Full Text: DOI
Celletti, Alessandra; Della Penna, Gabriella; Froeschlé, Claude Analytical approximation of the solution of the dissipative standard map. (English) Zbl 0997.37037 Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 12, 2471-2479 (1998). Reviewer: Messoud Efendiev (Berlin) MSC: 37J40 37E40 70F15 70H08 PDF BibTeX XML Cite \textit{A. Celletti} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 12, 2471--2479 (1998; Zbl 0997.37037) Full Text: DOI
Jorba, Àngel; Villanueva, Jordi Numerical computation of normal forms around some periodic orbits of the restricted three-body problem. (English) Zbl 0963.70508 Physica D 114, No. 3-4, 197-229 (1998). MSC: 70-08 70F07 70H05 PDF BibTeX XML Cite \textit{À. Jorba} and \textit{J. Villanueva}, Physica D 114, No. 3--4, 197--229 (1998; Zbl 0963.70508) Full Text: DOI
Chandre, C.; Jauslin, H. R. A version of Thirring’s approach to the Kolmogorov-Arnold-Moser theorem for quadratic Hamiltonians and degenerate twist. (English) Zbl 0927.37033 J. Math. Phys. 39, No. 11, 5856-5865 (1998). MSC: 37J40 70H05 37N05 70H08 PDF BibTeX XML Cite \textit{C. Chandre} and \textit{H. R. Jauslin}, J. Math. Phys. 39, No. 11, 5856--5865 (1998; Zbl 0927.37033) Full Text: DOI
Hanßmann, Heinz The quasi-periodic centre-saddle bifurcation. (English) Zbl 0936.37028 J. Differ. Equations 142, No. 2, 305-370 (1998). Reviewer: Alexei Ivanov (St.Peterburg) MSC: 37J40 37J35 37N05 37J20 PDF BibTeX XML Cite \textit{H. Hanßmann}, J. Differ. Equations 142, No. 2, 305--370 (1998; Zbl 0936.37028) Full Text: DOI
Guzzo, Massimilliano; Morbidelli, Alessandro Construction of a Nekhoroshev like result for the asteroid belt dynamical system. (English) Zbl 0883.58032 Celest. Mech. Dyn. Astron. 66, No. 3, 255-292 (1997). MSC: 37N99 70F15 PDF BibTeX XML Cite \textit{M. Guzzo} and \textit{A. Morbidelli}, Celest. Mech. Dyn. Astron. 66, No. 3, 255--292 (1997; Zbl 0883.58032) Full Text: DOI
Morbidelli, Alessandro; Guzzo, Massimiliano The Nekhoroshev theorem and the asteroid belt dynamical system. (English) Zbl 0891.70007 Celest. Mech. Dyn. Astron. 65, No. 1-2, 107-136 (1997). Reviewer: M.Calvo (Zaragoza) MSC: 70F15 37J40 34D10 PDF BibTeX XML Cite \textit{A. Morbidelli} and \textit{M. Guzzo}, Celest. Mech. Dyn. Astron. 65, No. 1--2, 107--136 (1997; Zbl 0891.70007) Full Text: DOI
Xu, Junxiang Persistence of elliptic lower dimensional invariant tori for small perturbation of degenerate integrable Hamiltonian systems. (English) Zbl 0889.58045 J. Math. Anal. Appl. 208, No. 2, 372-387 (1997). Reviewer: N.Medvedeva (Chelyabinsk) MSC: 37J35 37K10 37J40 34C05 34D10 34C40 PDF BibTeX XML Cite \textit{J. Xu}, J. Math. Anal. Appl. 208, No. 2, 372--387 (1997; Zbl 0889.58045) Full Text: DOI
Rudnev, M.; Wiggins, S. KAM theory near multiplicity one resonant surfaces in perturbations of a-priori stable Hamiltonian systems. (English) Zbl 0876.58015 J. Nonlinear Sci. 7, No. 2, 177-209 (1997). MSC: 37J99 37G05 37J35 37K10 37C55 37J40 70H05 70K30 PDF BibTeX XML Cite \textit{M. Rudnev} and \textit{S. Wiggins}, J. Nonlinear Sci. 7, No. 2, 177--209 (1997; Zbl 0876.58015) Full Text: DOI
Fassò, Francesco The Euler-Poinsot top: a non-commutatively integrable system without global action-angle coordinates. (English) Zbl 0895.70005 Z. Angew. Math. Phys. 47, No. 6, 953-976 (1996). Reviewer: Liu Yanzhu (Shanghai) MSC: 70E17 70G45 37J35 37K10 70H05 PDF BibTeX XML Cite \textit{F. Fassò}, Z. Angew. Math. Phys. 47, No. 6, 953--976 (1996; Zbl 0895.70005) Full Text: DOI
Morbidelli, Alessandro; Froeschlé, Claude On the relationship between Lyapunov times and macroscopic instability times. (English) Zbl 0880.58010 Celest. Mech. Dyn. Astron. 63, No. 2, 227-239 (1996). MSC: 37J99 82C41 PDF BibTeX XML Cite \textit{A. Morbidelli} and \textit{C. Froeschlé}, Celest. Mech. Dyn. Astron. 63, No. 2, 227--239 (1996; Zbl 0880.58010) Full Text: DOI
Laskar, Jacques Large scale chaos and marginal stability in the solar system. (English) Zbl 0886.70012 Celest. Mech. Dyn. Astron. 64, No. 1-2, 115-162 (1996). MSC: 70F15 37D45 37C75 PDF BibTeX XML Cite \textit{J. Laskar}, Celest. Mech. Dyn. Astron. 64, No. 1--2, 115--162 (1996; Zbl 0886.70012) Full Text: DOI
Froeschlé, C.; Lega, E. On the measure of the structure around the last KAM torus before and after its break-up. (English) Zbl 0880.58016 Celest. Mech. Dyn. Astron. 64, No. 1-2, 21-31 (1996). MSC: 37A99 PDF BibTeX XML Cite \textit{C. Froeschlé} and \textit{E. Lega}, Celest. Mech. Dyn. Astron. 64, No. 1--2, 21--31 (1996; Zbl 0880.58016) Full Text: DOI
Tompaidis, Stathis Numerical study of invariant sets of a quasiperiodic perturbation of a symplectic map. (English) Zbl 0868.58038 Exp. Math. 5, No. 3, 211-230 (1996). Reviewer: M.Puta (Timişoara) MSC: 37J99 PDF BibTeX XML Cite \textit{S. Tompaidis}, Exp. Math. 5, No. 3, 211--230 (1996; Zbl 0868.58038) Full Text: DOI EMIS EuDML
Gentile, G.; Mastropietro, V. KAM theorem revisited. (English) Zbl 0896.58030 Physica D 90, No. 3-4, 225-234 (1996). MSC: 37J99 81T17 70H05 PDF BibTeX XML Cite \textit{G. Gentile} and \textit{V. Mastropietro}, Physica D 90, No. 3--4, 225--234 (1996; Zbl 0896.58030) Full Text: DOI
Morbidelli, Alessandro; Giorgilli, Antonio Superexponential stability of KAM tori. (English) Zbl 1080.37512 J. Stat. Phys. 78, No. 5-6, 1607-1617 (1995). MSC: 37C55 PDF BibTeX XML Cite \textit{A. Morbidelli} and \textit{A. Giorgilli}, J. Stat. Phys. 78, No. 5--6, 1607--1617 (1995; Zbl 1080.37512) Full Text: DOI
Scherer, Wolfgang Superconvergent perturbation method in quantum mechanics. (English) Zbl 1020.81579 Phys. Rev. Lett. 74, No. 9, 1495-1499 (1995). MSC: 81Q15 PDF BibTeX XML Cite \textit{W. Scherer}, Phys. Rev. Lett. 74, No. 9, 1495--1499 (1995; Zbl 1020.81579) Full Text: DOI