Response solutions to the quasi-periodically forced systems with degenerate equilibrium: a simple proof of a result of W Si and J Si and extensions

DOI10.1088/1361-6544/ABBF33zbMath1473.37075arXiv1909.09915OpenAlexW3123686920MaRDI QIDQ5147945

Rafael de la Llave, Fenfen Wang, Hongyu Cheng

Publication date: 29 January 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.09915

zbMATH Keywords

fixed point theoremresponse solutionsdegenerate fixed pointssecond-order oscillators

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Fixed-point theorems (47H10) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (7)

The existence of almost periodic response solutions for superlinear Duffing's equations ⋮ Response solutions of degenerate quasi-periodic systems under small perturbations ⋮ Response solutions of 2-dimensional degenerate systems under quasi-periodic perturbations ⋮ Coexistence of hyperbolic and elliptic invariant tori for completely degenerate quasi-periodically forced maps ⋮ Parabolic invariant tori in quasi-periodically forced skew-product maps ⋮ Response solutions of 3-dimensional degenerate quasi-periodic systems with small parameter ⋮ Response solutions in degenerate oscillators under degenerate perturbations

Cites Work

• Construction of response functions in forced strongly dissipative systems
• Response Solutions to Quasi-Periodically Forced Systems, Even to Possibly Ill-Posed PDEs, with Strong Dissipation and any Frequency Vectors
• Nature of Singularities for Analyticity Domains of Invariant Curves
• Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems
• On the regularity of the composition of diffeomorphisms
• Response Solutions for Quasi-Periodically Forced, Dissipative Wave Equations
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