Convergent series for quasi-periodically forced strongly dissipative systems

DOI10.1142/S0219199713500223zbMath1306.34066arXiv1211.2125MaRDI QIDQ5170118

Roberto Feola, Livia Corsi, Guido Gentile

Publication date: 18 July 2014

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.2125

zbMATH Keywords

quasi-periodic solutionsquasi-periodic forcingnon-degeneracysmall divisorsstrongly dissipative systemsirrationality conditionsLindstet series

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27) Asymptotic expansions of solutions to ordinary differential equations (34E05) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Multifrequency systems of ordinary differential equations (34C46)

Related Items (8)

Response solutions for strongly dissipative quasi-periodically forced systems with arbitrary nonlinearities and frequencies ⋮ Response Solutions for Quasi-Periodically Forced, Dissipative Wave Equations ⋮ Response solutions in singularly perturbed, quasi-periodically forced nonlinear oscillators ⋮ Domains of analyticity and Lindstedt expansions of KAM tori in some dissipative perturbations of Hamiltonian systems ⋮ Response solutions for forced systems with large dissipation and arbitrary frequency vectors ⋮ Response Solutions to Quasi-Periodically Forced Systems, Even to Possibly Ill-Posed PDEs, with Strong Dissipation and any Frequency Vectors ⋮ Domains of analyticity for response solutions in strongly dissipative forced systems ⋮ Forced quasi-periodic oscillations in strongly dissipative systems of any finite dimension

Cites Work

• Oscillator synchronisation under arbitrary quasi-periodic forcing
• Resonances within chaos
• Quasi-periodic motions in strongly dissipative forced systems
• Summation of divergent series and Borel summability for strongly dissipative differential equations with periodic or quasiperiodic forcing terms
• Quasiperiodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems
• Invariant sets for the varactor equation
• Quasiperiodic motions in dynamical systems: Review of a renormalization group approach

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