SEMINAIRE MERCREDI 17 OCTOBRE 2007
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Alexei Vasiliev
Space Research Institute, Moscow

Title: Destruction of adiabatic invariance at resonances in slow-fast
Hamiltonian systems

Abstract:  In many problems one has to study dynamical systems where motions of
two types can be distinguished, namely, a slow one and a fast one.
Averaging over the fast motion can be used for approximate description
of the slow motion. First integrals of the averaged system are
approximate first integrals of the exact system, i.e. adiabatic
invariants. The averaging, however, fails to describe the dynamics
properly when the system passes through resonances. In the talk,
resonant phenomena in the fast motion (capture into resonance,
scattering on resonance) will be considered. These phenomena lead to
destruction of adiabatic invariance, dynamical chaos, and transport in
large domains in the phase space. The perturbation theory methods for
description of these phenomena will be outlined. As an example, we'll
consider the problem of surfatron acceleration of a relativistic
charged particle.