SEMINAIRE MERCREDI 28 JANVIER 2004
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Guillaume James
Département de Mathématiques, INSA de Toulouse

Title: Centre manifold reduction for time-periodic oscillations in infinite lattices

Summary: Time-periodic oscillations in infinite one-dimensional lattices can be
expressed in many cases as solutions of an ill-posed "spatial" recurrence relation
on a loop space. We give simple spectral conditions under which all small amplitude
solutions lie on an invariant finite-dimensional centre manifold. This result
reduces the problem locally to the study of a finite-dimensional mapping. In the
case of hardening Fermi-Pasta-Ulam chains, this map is reversible and admits
homoclinic orbits to 0 corresponding to "discrete breather" solutions.