Entropy collapse versus entropy rigidity for Reeb and Finsler flows

• Alberto Abbondandolo ^[1] ; Marcelo R. R. Alves ^[2] ; Murat Săglam ^[3] ; Felix Schlenk ^[4]
  1. [1] Ruhr University Bochum

     Ruhr University Bochum

     Kreisfreie Stadt Bochum, Alemania

     
  2. [2] University of Antwerp

     University of Antwerp

     Arrondissement Antwerpen, Bélgica

     
  3. [3] University of Cologne

     University of Cologne

     Kreisfreie Stadt Köln, Alemania

     
  4. [4] University of Neuchâtel

     University of Neuchâtel

     Neuchâtel, Suiza

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 5, 2023
• Idioma: inglés
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• Resumen

  • On every closed contact manifold there exist contact forms with volume one whose Reeb flows have arbitrarily small topological entropy. In contrast, for many closed manifolds there is a uniform positive lower bound for the topological entropy of (not necessarily reversible) normalized Finsler geodesic flows.