Séminaire de Géométrie, Groupes et Dynamique
# Marcelo Alves: "Hofer's geometry and braid stability"

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Europe/Paris

435 (UMPA)
### 435

#### UMPA

Description

The Hofer’s metric dH is a remarkable bi-invariant metric on the group of Hamiltonian diffeomorphisms of a symplectic manifold. In my talk, I will explain a result, obtained jointly with Matthias Meiwes, which says that the braid type of a set of periodic orbits of a Hamiltonian diffeomorphism on a closed surface is stable under perturbations that are sufficiently small with respect to Hofer’s metric. As a consequence of this we obtained that the topological entropy, seen as a function on the space of Hamiltonian diffeomorphisms of a closed surface, is lower semi-continuous with respect to the Hofer metric dH.

If time permits, I will explain related questions for Reeb flows on 3-manifolds and Hamiltonian diffeomorphisms on higher-dimensional symplectic manifolds, and recent progress on these problems obtained by myself, Meiwes, Abror Pirnapasov and Lucas Dahinden.