General KAM theorems and their applications to invariant tori with prescribed frequencies

DOI10.1134/S1560354716010068zbMath1344.37070arXiv1504.00726OpenAlexW1593315443MaRDI QIDQ283036

Junxiang Xu, Xuezhu Lu

Publication date: 13 May 2016

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.00726

zbMATH Keywords

Hamiltonian systeminvariant toriKAM iterationnondegeneracy condition

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) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (9)

A new KAM theorem for the hyperbolic lower dimensional tori in reversible systems ⋮ A KAM theorem for quasi-periodic non-twist mappings and its application ⋮ A KAM theorem for lower dimensional elliptic invariant tori of nearly integrable symplectic mappings ⋮ Partial preservation of frequencies and Floquet exponents of invariant tori in the reversible KAM context 2 ⋮ Boundedness of semilinear Duffing equations with Liouvillean frequency ⋮ A formal KAM theorem for Hamiltonian systems and its application to hyperbolic lower dimensional invariant tori ⋮ On the reducibility of 2-dimensional linear quasi-periodic systems with small parameters ⋮ Existence of invariant curves for area-preserving mappings under weaker non-degeneracy conditions ⋮ Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter

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