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Let M be a smooth closed manifold and T*M its cotangent bundle endowed withthe usual symplectic structure. A hypersurface S in T*M is said to be fiberwisestarshaped if for each point q in M the intersection of S with the fiber at qis starshaped with respect to the origin. In this thesis we give lower boundsof the growth rate of the number of closed Reeb orbits on a fiberwisestarshaped 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 hasan exponential growth of conjugacy classes or not. If the base space M issimply connected we generalize the theorem of Ballmann and Ziller on the growthof closed geodesics to Reeb flows.

The Weinstein conjecture with multiplicities on spherizations