SEMINAIRE MERCREDI 18 OCTOBRE 2006
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Julien Tailleur
PMMH-ESPCI, Paris

Title: Revealing structures of atypical chaoticity with a Lyapunov weighted dynamics

Abstract: Structures with atypical chaoticity play a crucial role in many
physical situations. For instance, resonances and separatrices
determine the fate of planetary systems, and localised objects like
solitons and breathers provide mechanisms of energy transport in
nonlinear systems such as Bose-Einstein condensates and biological
molecules. Unfortunately, despite the fundamental progress made in the
last years, most of the numerical methods to locate these 'rare'
trajectories are confined to low-dimensional or toy models, while more
realistic systems are still hard to reach.

Here I present a new method that allows one to work in higher
dimensions by selecting trajectories with unusual chaoticity. As an
example, I study the Fermi-Pasta-Ulam nonlinear chain in equilibrium
and show that the algorithm rapidly singles out soliton and chaotic
breathers, when searching for trajectories with low and high level of
chaoticity, respectively.