Quasi-periodic solutions and stability of the equilibrium for quasi-periodically forced planar reversible and Hamiltonian systems under the Bruno condition

DOI10.1088/0951-7715/23/3/007zbMath1196.37101OpenAlexW1974936024MaRDI QIDQ3550005

Heinz Hanßmann, Jian-guo Si

Publication date: 30 March 2010

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/48970060f1cb84d1004fd50b47d64154860acbdd

zbMATH Keywords

periodic solutionshomogenizationperturbationsnormal formsKAM theoryFourier coefficientsnonautonomous dynamical systemssmall divisorsArnol'd diffusionspecial Fourier seriespartial differential equations in media with periodic structureFourier series of functions with special properties

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

Related Items (11)

On invariant tori with prescribed frequency in Hamiltonian systems ⋮ Quasi-periodic solutions for quasi-periodically forced nonlinear Schrödinger equations with quasi-periodic inhomogeneous terms ⋮ Response solutions for strongly dissipative quasi-periodically forced systems with arbitrary nonlinearities and frequencies ⋮ Elliptic-type degenerate invariant tori for quasi-periodically forced four-dimensional non-conservative systems ⋮ Quasi-periodic solutions of a non-autonomous wave equations with quasi-periodic forcing ⋮ Quasi-periodic bifurcations in reversible systems ⋮ Quasi-periodic perturbations within the reversible context 2 in KAM theory ⋮ Dynamical stability of quasi-periodic response solutions in planar conservative systems ⋮ Persistence of degenerate lower dimensional invariant tori in reversible systems with Bruno non-degeneracy conditions ⋮ Almost periodic solutions for a class of linear Schrödinger equations with almost periodic forcing ⋮ Analytic solutions of a second-order functional differential equation

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