Positive topological entropy of Reeb flows on spherizations

2010/08/26 by Leonardo Macarini, Felix Schlenk · 2 citations
Mathematics · #math.DS #math.SG

paper · pdf · doi:10.1017/s0305004111000119

29 pages, 3 figures

arxiv created 2010/08/26 · arxiv updated 2015/05/19

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.

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