Faculté des sciences

## The Weinstein conjecture with multiplicities on spherizations

### Thèse de doctorat : Université de Neuchâtel, 2011.

Let M be a smooth closed manifold and T∗M its cotangent bundle endowed with the usual symplectic structure ω = dλ, where λ is the Liouville form. A hypersurface Σ ⊂ T∗M is said to be fiberwise starshaped if for each point q ∈ M the intersection Σ q := Σ∩T∗qM of Σ with... Plus

Ajouter à la liste personnelle

# Exporter vers

Summary
Let M be a smooth closed manifold and T∗M its cotangent bundle endowed with the usual symplectic structure ω = dλ, where λ is the Liouville form. A hypersurface Σ ⊂ T∗M is said to be fiberwise starshaped if for each point qM the intersection Σ q := Σ∩T∗qM of Σ with the fiber at q is the smooth boundary of a domain in T∗M which is starshaped with respect to the origin 0qT∗qM.

In this thesis we give lower bounds on the growth rate of the number of closed Reeb orbits on a fiberwise starshaped hypersurface in terms of the topology of the free loop space of M. We distinguish the two cases that the fundamental group of the base space M has an exponential growth of conjugacy classes or not. If the base space M is simply connected we generalize the theorem of Ballmann and Ziller on the growth of closed geodesics to Reeb flows.