Entropy collapse versus entropy rigidity for Reeb and Finsler flows

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 geodes...

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Veröffentlicht in:	Selecta mathematica (Basel, Switzerland) Switzerland), 2023-11, Vol.29 (5), Article 67
Hauptverfasser:	Abbondandolo, Alberto, Alves, Marcelo R. R., Sağlam, Murat, Schlenk, Felix
Format:	Artikel
Sprache:	eng
Schlagworte:	Entropy Lower bounds Mathematics Mathematics and Statistics Topology
Online-Zugang:	Volltext
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Zusammenfassung:	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.
ISSN:	1022-1824 1420-9020
DOI:	10.1007/s00029-023-00865-8