On the Destruction of Resonant Lagrangean Tori in Hamiltonian Systems

DOI10.1007/978-3-0348-0451-6_13zbMath1314.37044OpenAlexW2187938394MaRDI QIDQ5253371

Heinz Hanßmann, Jiangong You, Henk W. Broer

Publication date: 5 June 2015

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-0348-0451-6_13

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items

Resonance and fractal geometry, Response solutions in singularly perturbed, quasi-periodically forced nonlinear oscillators, Quasi-periodic bifurcations in reversible systems, Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems, Completely degenerate responsive tori in Hamiltonian systems, Moser's theorem for hyperbolic-type degenerate lower tori in Hamiltonian system, The quasi-periodic centre-saddle bifurcation, Response solutions in degenerate oscillators under degenerate perturbations, Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter, Perturbations of superintegrable systems, Resonance and Singularities

Cites Work

• Dynamical systems VIII. Singularity theory. II: Classification and applications. Transl. from the Russian by J. S. Joel
• Umbilical torus bifurcations in Hamiltonian systems
• Local and semi-local bifurcations in Hamiltonian dynamical systems. Results and examples
• Normal linear stability of quasi-periodic tori
• Quasi-periodic stability of normally resonant tori
• Singularites \(C^\infty\) en presence de symétrie. En particulier en presence de la symétrie d'un groupe de Lie compact
• The quasi-periodic centre-saddle bifurcation
• A KAM theorem for hyperbolic-type degenerate lower dimensional tori in Hamiltonian systems
• The surviving of lower dimensional tori from a resonant torus of Hamiltonian systems
• Lower dimensional invariant tori in the regions of instability for nearly integrable Hamiltonian systems
• KAM-type theorem on resonant surfaces for nearly integrable Hamiltonian systems
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• Birkhoff-Kolmogorov-Arnold-Moser tori in convex Hamiltonian systems
• Quasi-periodic motions in families of dynamical systems. Order amidst chaos
• Integrability of hamiltonian systems on cantor sets
• Fractional Lindstedt series
• Melnikov theory to all orders and Puiseux series for subharmonic solutions
• From a differentiable to a real analytic perturbation theory, applications to the Kupka Smale theorems
• Generic Hamiltonian dynamical systems are neither integrable nor ergodic
• Differential Topology
• Bifurcations of normally parabolic tori in Hamiltonian systems
• Unfoldings and bifurcations of quasi-periodic tori
• A degenerate bifurcation in the Hénon-Heiles family
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