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The Weinstein conjecture with multiplicities on spherizations
Auteur(s)
Heistercamp, Muriel
Editeur(s)
Bourgeois, F.
Gutt, S.
Abbondandolo, A.
Bertelson, M.
Date de parution
2011
Résumé
Let <i>M</i> be a smooth closed manifold and <i>T∗M</i> its cotangent bundle endowed with the usual symplectic structure <i>ω = dλ</i>, where <i>λ</i> is the Liouville form. A hypersurface Σ ⊂ <i>T∗M</i> is said to be <i>fiberwise starshaped</i> if for each point <i>q</i> ∈ <i>M</i> the intersection Σ <i><sub>q</sub></i> := Σ∩<i>T∗<sub>q</sub>M</i> of Σ with the fiber at <i>q</i> is the smooth boundary of a domain in <i>T∗M</i> which is starshaped with respect to the origin 0<i><sub>q</sub></i> ∈ <i>T∗<sub>q</sub>M</i>. <br><br> In this thesis we give lower bounds on the growth rate of the number of closed Reeb orbits on a <i>fiberwise starshaped hypersurface</i> in terms of the topology of the free loop space of <i>M</i>. We distinguish the two cases that the fundamental group of the base space <i>M</i> has an exponential growth of conjugacy classes or not. If the base space <i>M</i> is simply connected we generalize the theorem of Ballmann and Ziller on the growth of closed geodesics to Reeb flows.
Notes
Thèse de doctorat : Université de Neuchâtel, 2011
Identifiants
Type de publication
doctoral thesis
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