Measures of maximal entropy for surface diffeomorphisms

We show that $C^\infty$ surface diffeomorphisms with positive topological entropy have at most finitely many ergodic measures of maximal entropy in general, and at most one in the topologically transitive case. This answers a question of Newhouse, who proved that such measures always exist. To do th...

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Veröffentlicht in:	Annals of mathematics 2022-03, Vol.195 (2), p.421-508
Hauptverfasser:	Buzzi, Jérôme, Crovisier, Sylvain, Sarig, Omri
Format:	Artikel
Sprache:	eng
Schlagworte:	Dynamical Systems Mathematics
Online-Zugang:	Volltext
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