Chaotic resonant dynamics and exchanges of energy in Hamiltonian PDEs

Filippo Giuliani, Marcel Guardia, Pau Martin, Stefano Pasquali

Research output: Contribution to journalArticlepeer-review

Abstract

The aim of this note is to present the recent results in [16] where we provide the existence of solutions of some nonlinear resonant PDEs on T2 exchanging energy among Fourier modes in a "chaotic-like" way. We say that a transition of energy is "chaotic-like" if either the choice of activated modes or the time spent in each transfer can be chosen randomly. We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations. The key point of the construction of the special solutions is the existence of heteroclinic connections between invariant objects and the construction of symbolic dynamics (a Smale horseshoe) for the Birkho. Normal Form of those equations.

Original languageEnglish
Pages (from-to)149-166
Number of pages18
JournalAtti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Volume32
Issue number1
DOIs
Publication statusPublished - 2021 Apr

Subject classification (UKÄ)

  • Mathematics

Free keywords

  • Birkho. normal form
  • Hamiltonian PDEs
  • Transfer of energy

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