Lower-dimensional invariant tori for a class of degenerate reversible systems under small perturbations

DOI10.1090/PROC/17051MaRDI QIDQ6654039

Xiao-Mei Yang, Junxiang Xu

Publication date: 18 December 2024

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

invariant torireversible systemKAM iterationdegenerate equilibrium point

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)

Cites Work

• Construction of response solutions for two classes of quasi-periodically forced four-dimensional nonlinear systems with degenerate equilibrium point under small perturbations
• Invariant manifolds at infinity of the RTBP and the boundaries of bounded motion
• Invariant m-dimensional tori of reversible systems with phase space of dimension greater than 2m
• Completely degenerate lower-dimensional invariant tori for Hamiltonian system
• Persistence of multi-dimensional degenerate hyperbolic lower dimensional invariant tori in reversible systems
• Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems
• Convergent series expansions for quasi-periodic motions
• On the persistence of degenerate lower-dimensional tori in reversible systems
• Biasymptotic solutions of perturbed integrable Hamiltonian systems
• The iteration-approximation decoupling in the reversible KAM theory
• Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems
• Completely degenerate responsive tori in Hamiltonian systems
• On lower dimensional invariant tori in reversible systems
• Oscillatory motions for the restricted planar circular three body problem
• Persistence of multiscale degenerate invariant tori for reversible systems with multiscale degenerate equilibrium points
• Persistence of degenerate lower dimensional invariant tori with prescribed frequencies in reversible systems

This page was built for publication: Lower-dimensional invariant tori for a class of degenerate reversible systems under small perturbations

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6654039)