Displaying similar documents to “On classical series expansions for quasi-periodic motions.”

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.

Periodic solutions for second order Hamiltonian systems on an arbitrary energy surface

Chengfu Che, Xiaoping Xue (2012)

Annales Polonici Mathematici


Two theorems about the existence of periodic solutions with prescribed energy for second order Hamiltonian systems are obtained. One gives existence for almost all energies under very natural conditions. The other yields existence for all energies under a further condition.

Periodic orbits close to elliptic tori and applications to the three-body problem

Massimiliano Berti, Luca Biasco, Enrico Valdinoci (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze


We prove, under suitable non-resonance and non-degeneracy “twist” conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period...