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On the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with compact center leaves

Rocha, Joas Elias ; Tahzibi, Ali

Mathematische Zeitschrift, 2022-05, Vol.301 (1), p.471-484 [Periódico revisado por pares]

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Título:
On the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with compact center leaves
Autor: Rocha, Joas Elias ; Tahzibi, Ali
Assuntos: Entropy ; Ergodic processes ; Isomorphism ; Mathematics ; Mathematics and Statistics ; Toruses ; Upper bounds
É parte de: Mathematische Zeitschrift, 2022-05, Vol.301 (1), p.471-484
Descrição: In this paper we study the number of ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms defined on 3-torus with compact center leaves. Assuming the existence of a periodic leaf with Morse–Smale dynamics we prove a sharp upper bound for the number of maximal measures in terms of the number of sources and sinks of Morse–Smale dynamics. A well-known class of examples for which our results apply are the so called Kan-type diffeomorphisms admitting physical measures with intermingled basins.
Editor: Berlin/Heidelberg: Springer Berlin Heidelberg
Idioma: Inglês

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