2011/05/19 by Muriel Heistercamp, Heistercamp, Muriel · 1 citation
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.SG
paper · pdf · doi:10.48550/arxiv.1105.3886
Université Libre de Bruxelles et Université de Neuchâtel. PhD Thesis. 2011
arxiv created 2011/05/19 · openalex publication_date 2011/05/19 · arxiv updated 2015/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a smooth closed manifold and T*M its cotangent bundle endowed with the usual symplectic structure. A hypersurface S in T*M is said to be fiberwise starshaped if for each point q in M the intersection of S with the fiber at q is starshaped with respect to the origin. In this thesis we give lower bounds of 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.