Invariant curves of smooth quasi-periodic mappings

DOI10.3934/dcds.2018006zbMath1372.37088arXiv1705.08762OpenAlexW2963594806MaRDI QIDQ2409070

Peng Huang, Xiong Li, Bin Liu

Publication date: 10 October 2017

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.08762

zbMATH Keywords

invariant curvesquasi-periodic mappings

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical aspects of twist maps (37E40)

Related Items (11)

Boundedness of solutions of a quasi-periodic sublinear Duffing equation ⋮ Persistence of invariant tori in integrable Hamiltonian systems under almost periodic perturbations ⋮ A KAM theorem for quasi-periodic non-twist mappings and its application ⋮ Existence of invariant curves for degenerate quasi-periodic reversible mappings ⋮ Existence of invariant curves for degenerate almost periodic reversible mappings ⋮ Invariant curves of almost periodic twist mappings ⋮ Almost periodic solutions for an asymmetric oscillation ⋮ Response solutions for finite smooth harmonic oscillators with quasi-periodic forcing ⋮ Existence of invariant curves with prescribed frequency for degenerate area preserving mappings ⋮ Existence of periodically invariant tori on resonant surfaces for twist mappings ⋮ Three examples in the dynamical systems theory

Cites Work

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• Lectures on celestial mechanics. Transl. from the German by C. I. Kalme.
• Moser's theorem for lower dimensional tori
• Quasi-periodic solutions for an asymmetric oscillation
• A stability theorem for minimal foliations on a torus
• Generalized implicit function theorems with applications to some small divisor problems, I
• Invariant curve theorem for quasiperiodic twist mappings and stability of motion in the Fermi-Ulam problem
• Invariant curves of quasi-periodic reversible mappings

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