Chaotic-like transfers of energy in Hamiltonian PDEs
Analysis of PDEs
2021-02-24 v1 Dynamical Systems
Abstract
We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange can be considered \emph{chaotic-like} since either the choice of activated modes or the time spent in each transfer can be chosen randomly. The key point of the construction of those orbits is the existence of heteroclinic connections between invariant objects and the construction of symbolic dynamics (a Smale horseshoe) for the Birkhoff Normal Form truncation of those equations.
Keywords
Cite
@article{arxiv.2006.09309,
title = {Chaotic-like transfers of energy in Hamiltonian PDEs},
author = {Filippo Giuliani and Marcel Guardia and Pau Martin and Stefano Pasquali},
journal= {arXiv preprint arXiv:2006.09309},
year = {2021}
}