Representation of non-Hamiltonian vector fields in the coordinates of the observer via the isosymplectic geometry.
Representation theory of finite Abelian groups applied to a linear diatomic crystal.
Resonant normal form for even periodic FPU chains
Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcé
Henri Poincaré avait déjà remarqué que les variétés stable et instable du pendule perturbé, défini par l’hamiltonienne coïncident pas lorsque que le paramètre n’est pas nul, mais qu’on peut leur associer un même développement formel divergent en puissance de . Cette divergence est ici analysée au moyen de la récente théorie de la résurgence, et du calcul étranger qui permet de trouver un équivalent asymptotique de l’écart des deux variétés pour tendant vers zéro - du moins cela est-il montré...
Retracts, fixed point index and differential equations.
Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions.
Robust transitivity in hamiltonian dynamics
A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce open sets () of symplectic diffeomorphisms and Hamiltonian systems, exhibitinglargerobustly transitive sets. We show that the closure of such open sets contains a variety of systems, including so-calleda priori unstable integrable systems. In addition, the existence of ergodic measures with large support is obtained for all those systems. A main ingredient of...
Root systems and hypergeometric functions IV
Rotation numbers for Lagrangian systems and Morse theory