Displaying similar documents to “Periodicity and transport from round-off errors.”

Quasi-periodic solutions of PDEs

Massimiliano Berti (2011-2012)

Séminaire Laurent Schwartz — EDP et applications


The aim of this talk is to present some recent existence results about quasi-periodic solutions for PDEs like nonlinear wave and Schrödinger equations in 𝕋 d , d 2 , and the 1 - d derivative wave equation. The proofs are based on both Nash-Moser implicit function theorems and KAM theory.

Quasi-periodic oscillations for wave equations under periodic forcing

Massimiliano Berti, Michela Procesi (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni


Existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced, nonlinear wave equations with periodic spatial boundary conditions is established. We consider both the cases the forcing frequency is (Case A) a rational number and (Case B) an irrational number.

Invariant tori for periodically perturbed oscillators.

Carmen Chicone (1997)

Publicacions Matemàtiques


The response of an oscillator to a small amplitude periodic excitation is discussed. In particular, sufficient conditions are formulated for the perturbed oscillator to have an invariant torus in the phase cylinder. When such an invariant torus exists, some perturbed solutions are in the basin of attraction of this torus and are thus entrained to the dynamical behavior of the perturbed system on the torus. In particular, the perturbed solutions in the basin of attraction of the invariant...