Forced quasi-periodic oscillations in strongly dissipative systems of any finite dimension

DOI10.1142/S0219199718500645zbMath1439.70029arXiv1710.01266OpenAlexW2964173604MaRDI QIDQ5237239

Alessandro Mazzoccoli, Faenia Vaia, Guido Gentile

Publication date: 17 October 2019

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

Full work available at URL: https://arxiv.org/abs/1710.01266

zbMATH Keywords

quasi-periodic forcingtree representationnon-degeneracy conditionstrongly dissipative systemsresponse solution

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Perturbations of ordinary differential equations (34D10) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Multifrequency systems of ordinary differential equations (34C46)

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Response solutions for strongly dissipative quasi-periodically forced systems with arbitrary nonlinearities and frequencies ⋮ Response solutions for degenerate reversible harmonic oscillators with zero-average perturbation ⋮ Response solutions for wave equations with variable wave speed and periodic forcing ⋮ Quasi-periodic traveling waves for forced Kirchhoff equations with strong damping on flat tori ⋮ Completely degenerate responsive tori in Hamiltonian systems ⋮ Response Solutions to Quasi-Periodically Forced Systems, Even to Possibly Ill-Posed PDEs, with Strong Dissipation and any Frequency Vectors ⋮ Stoker's Problem for Quasi-periodically Forced Reversible Systems with Multidimensional Liouvillean Frequency

Cites Work

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• Construction of response functions in forced strongly dissipative systems
• Multifrequency oscillations of singularly perturbed systems
• Resonant tori of arbitrary codimension for quasi-periodically forced systems
• Globally and locally attractive solutions for quasi-periodically forced systems
• KAM for the nonlinear Schrödinger equation
• Singularities and groups in bifurcation theory. Volume I
• Dynamical bifurcation of multifrequency oscillations in a fast-slow system
• Periodic solutions for a class of nonlinear partial differential equations in higher dimension
• Construction of quasi-periodic response solutions in forced strongly dissipative systems
• Response solutions for forced systems with large dissipation and arbitrary frequency vectors
• 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
• Forced quasiperiodic and almost periodic solution for nonlinear systems
• Convergent series for quasi-periodically forced strongly dissipative systems
• Dynamic Response of Linear Mechanical Systems
• Mechanical Systems
• On limit cycles in systems of differential equations with a small parameter in the highest derivatives
• Domains of analyticity for response solutions in strongly dissipative forced systems