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On the barcode entropy of Reeb flows

  • Erman Çineli [1] ; Viktor L. Ginzburg [3] ; Başak Z. Gürel [4] ; Marco Mazzucchelli [2]
    1. [1] Swiss Federal Institute of Technology in Zurich

      Swiss Federal Institute of Technology in Zurich

      Zürich, Suiza

    2. [2] Centre National de la Recherche Scientifique

      Centre National de la Recherche Scientifique

      París, Francia

    3. [3] Department of Mathematics, UC Santa Cruz, USA
    4. [4] Department of Mathematics, UCF, Orlando, USA
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  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 4, 2025
  • Idioma: inglés
  • DOI: 10.1007/s00029-025-01062-5
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  • Resumen

    • 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.

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