On the Barcode Entropy of Reeb Flows

Abstract

In this paper we continue investigating connections between Floer theory and dynamics of Hamiltonian systems, focusing on the barcode entropy of Reeb flows. Barcode entropy is the exponential growth rate of the number of not-too-short bars in the Floer or symplectic homology persistence module. The key novel result is that the barcode entropy is bounded from below by the topological entropy of any hyperbolic invariant set. This, combined with the fact that the topological entropy bounds the barcode entropy from above, established by Fender, Lee and Sohn, implies that in dimension three the two types of entropy agree. The main new ingredient of the proof is a variant of the Crossing Energy Theorem for Reeb flows.

31 pages; final version (revised); as appeared in Selecta Mathematica

References in corpus (14)

• Floer homology and the heat flow
• Symbolic dynamics for three dimensional flows with positive topological entropy
• Hamiltonian Pseudo-rotations of Projective Spaces
• Positive topological entropy of Reeb flows on spherizations
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• Cylindrical contact homology and topological entropy
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• Topological spaces of persistence modules and their properties
• Target-local Gromov compactness
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• On hyperbolic points and periodic orbits of symplectomorphisms
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• Barcode entropy of geodesic flows
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Cited by in corpus (2)

• Barcode entropy for Reeb flows on contact manifolds with Liouville fillings
• Invariant Sets and Hyperbolic Closed Reeb Orbits