SEMINAIRE MERCREDI 23 JANVIER 2008
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Guido Gentile
Math Depart, Univ Roma3, Italie

Title: Self-energy resummation and Borel summability for
quasi-periodic motions

Abstract: In this talk I will consider some dynamical systems with a
suitable small parameter, where quasi-periodic motions naturally
arise. Examples are provided by lower-dimensional tori and strongly
dissipative systems with a periodic or quasi-periodic forcing. Even
working in the analytic setting, such solutions in general are not
expected to be analytic in the parameter. However the perturbation
series are well defined to all orders and can be given a meaning by
means of a summation criterion which can be interpreted as a summation
of self-energy graphs in quantum field theory. In certain cases one
can prove that the perturbation series are Borel-summable.