On some completions of the space of Hamiltonian maps

Vincent Humilière (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

We study the completions of the space of Hamiltonian diffeomorphisms of the standard linear symplectic space, for Viterbo's distance and some others derived from it, we study their different inclusions and give some of their properties. In particular, we give a convergence criterion for these distances. This allows us to prove that the completions contain non-ordinary elements, as for example, discontinuous Hamiltonians. We also prove that some dynamical properties of Hamiltonian systems are preserved in the completions.

Domaines: Géométrie symplectique [math.SG]; Equations aux dérivées partielles [math.AP]

Vincent Humilière. On some completions of the space of Hamiltonian maps. Bulletin de la société mathématique de France, 2008, 136 (3), pp.373-404. ⟨hal-00014000v3⟩