Cylindrical contact homology and topological entropy

Abstract

We establish a relation between the growth of the cylindrical contact homology of a contact manifold and the topological entropy of Reeb flows on this manifold. We show that if a contact manifold $(M,\xi )$ admits a hypertight contact form ${\lambda }_0$ for which the cylindrical contact homology has exponential homotopical growth rate, then the Reeb flow of every contact form on $(M,\xi )$ has positive topological entropy. Using this result, we provide numerous new examples of contact 3-manifolds on which every Reeb flow has positive topological entropy.

42 pages, 2 figures. Exposition improved. Comments are welcome!

References in corpus (5)

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• Positive topological entropy of Reeb flows on spherizations
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Cited by in corpus (7)

• $C^0$-Stability of Topological Entropy for Contactomorphisms
• Bott-integrable Reeb flows on 3-manifolds
• On the Barcode Entropy of Reeb Flows
• A comparison of categorical and topological entropies on Weinstein manifolds
• Barcode entropy for Reeb flows on contact manifolds with Liouville fillings
• Some constructions of Weinstein manifolds with chaotic Reeb dynamics
• On the Integrability of codimension-one invariant subbundles of partially hyperbolic skew-products