Construction of quasi-periodic response solutions in forced strongly dissipative systems

DOI10.1515/form.2011.084zbMath1280.70012arXiv0910.0746OpenAlexW1985384346MaRDI QIDQ2905095

Guido Gentile

Publication date: 24 August 2012

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.0746

zbMATH Keywords

existencedivergent seriesrenormalisation groupdegenerate implicit function equation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Forced motions for nonlinear problems in mechanics (70K40) Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (15)

Almost periodic solutions in forced harmonic oscillators with infinite frequencies ⋮ Response solutions for strongly dissipative quasi-periodically forced systems with arbitrary nonlinearities and frequencies ⋮ Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems ⋮ Response solutions in singularly perturbed, quasi-periodically forced nonlinear oscillators ⋮ Response solutions for degenerate reversible harmonic oscillators with zero-average perturbation ⋮ Response solutions for finite smooth harmonic oscillators with quasi-periodic forcing ⋮ The existence of almost periodic response solutions for superlinear Duffing's equations ⋮ Response solutions for forced systems with large dissipation and arbitrary frequency vectors ⋮ Completely degenerate responsive tori in Hamiltonian systems ⋮ Parabolic invariant tori in quasi-periodically forced skew-product maps ⋮ Construction of response solutions for two classes of quasi-periodically forced four-dimensional nonlinear systems with degenerate equilibrium point under small perturbations ⋮ Oscillator synchronisation under arbitrary quasi-periodic forcing ⋮ Quasi-periodic response solutions in forced reversible systems with Liouvillean frequencies ⋮ Response solutions in degenerate oscillators under degenerate perturbations ⋮ Forced quasi-periodic oscillations in strongly dissipative systems of any finite dimension

Cites Work

• Stability for quasi-periodically perturbed Hill's equations
• Globally and locally attractive solutions for quasi-periodically forced systems
• Computation of quasi-periodic solutions of forced dissipative systems
• Computation of quasi-periodic solutions of forced dissipative systems II
• Quasi-periodic motions in strongly dissipative forced systems
• Fractional Lindstedt series
• Quasiperiodic attractors, Borel summability and the Bryuno condition for strongly dissipative systems
• Melnikov theory to all orders and Puiseux series for subharmonic solutions
• Algorithms for computing almost periodic steady-state response of nonlinear systems to multiple input frequencies

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