Positive topological entropy of Reeb flows on spherizations

Abstract

Let M be a closed manifold whose based loop space is ``complicated''. Examples are rationally hyperbolic manifolds and manifolds whose fundamental group has exponential growth. We prove that the topological entropy of any Reeb flow on the spherization of T*M is positive. Moreover, given q in M, for almost every q' in M the number of Reeb orbits from the fiber over q to the fiber over q' grows exponentially in time. If M is a surface of higher genus, we also obtain exponential growth of the number of closed Reeb orbits.

29 pages, 3 figures

References in corpus (5)

• Functors and Computations in Floer homology with Applications Part II
• Reeb vector fields and open book decompositions
• Magnetic flows on Sol-manifolds: dynamical and symplectic aspects
• On the stability of Mañé critical hypersurfaces
• The Weinstein conjecture with multiplicities on spherizations

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