Publications

URI permanent de cette collection

https://libra.unine.ch/handle/123456789/2

Parcourir par

Parcourir la collection Publications par Auteur "Abbondandolo, A."

Voici les éléments 1 - 1 sur 1
  • Publication
    Accès libre
    The Weinstein conjecture with multiplicities on spherizations
    Heistercamp, Muriel
    ;
    Schlenk, Félix 
    ;
    Bourgeois, F.
    ;
    Valette, Alain 
    ;
    Gutt, S.
    ;
    Abbondandolo, A.
    ;
    Bertelson, M.
    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 the fiber at q is the smooth boundary of a domain in T∗M which is starshaped with respect to the origin 0q ∈ T∗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.