10 papers
Arnold diffusion in Hamiltonian systems on infinite lattices
Filippo Giuliani, Marcel Guardia
We consider a system of infinitely many penduli on an -dimensional lattice with a weak coupling. For any prescribed path in the lattice, for suitable couplings, we construct orb…
Time Quasi-Periodic Traveling Gravity Water Waves in Infinite Depth
Roberto Feola, Filippo Giuliani
We present the recent result [8] concerning the existence of quasi-periodic in time traveling waves for the 2d pure gravity water waves system in infinite depth. We provide the fir…
Chaotic Resonant Dynamics and Exchanges of Energy in Hamiltonian PDEs
Filippo Giuliani, Marcel Guardia, Pau Martin +1
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 the 2-dimensional torus exchanging ener…
Transfers of energy through fast diffusion channels in some resonant PDEs on the circle
Filippo Giuliani
In this paper we consider two classes of resonant Hamiltonian PDEs on the circle with non-convex (respect to actions) first order resonant Hamiltonian. We show that, for appropriat…
Chaotic-like transfers of energy in Hamiltonian PDEs
Filippo Giuliani, Marcel Guardia, Pau Martin +1
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 b…
Reducible KAM tori for Degasperis-Procesi equation
Roberto Feola, Filippo Giuliani, Michela Procesi
We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian perturbations of the dispersive Degasperis-Procesi equation on the circle. The overall strategy…