Persistence of lower dimensional tori for a class of nearly integrable reversible systems

DOI10.1007/s10440-011-9615-9zbMath1223.37075OpenAlexW2001155111MaRDI QIDQ634693

Xiaocai Wang, Dongfeng Zhang, Junxiang Xu

Publication date: 16 August 2011

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-011-9615-9

zbMATH Keywords

reversible systemsinvariant toriKAM iteration

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27)

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A new KAM theorem for the hyperbolic lower dimensional tori in reversible systems, A new KAM iteration with nearly infinitely small steps in reversible systems of polynomial character, On the persistence of degenerate lower-dimensional tori in reversible systems, Non-Floquet invariant tori in reversible systems, Persistence of multiscale degenerate invariant tori for reversible systems with multiscale degenerate equilibrium points, Persistence of lower dimensional invariant tori in a class of reversible systems, Degenerate lower dimensional tori in reversible systems, On the persistence of lower-dimensional tori in reversible systems with hyperbolic-type degenerate equilibrium point under small perturbations, A KAM theorem for the elliptic lower dimensional tori with one normal frequency in reversible systems, On the persistence of lower-dimensional tori in reversible systems with high dimensional degenerate equilibrium under small perturbations, Completely degenerate lower-dimensional invariant tori in reversible systems, On the persistence of lower-dimensional elliptic tori with prescribed frequencies in reversible systems

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