Faculté des sciences

The Weinstein conjecture with multiplicities on spherizations

Heistercamp, Muriel ; Schlenk, Felix (Dir.) ; Bourgeois, F. (Codir.) ; Valette, Alain (Codir.) ; Gutt, S. (Codir.) ; Abbondandolo, A. (Codir.) ; Bertelson, M. (Codir.)

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

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    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.