Topological entropy and partially hyperbolic diffeomorphisms

Yongxia Hua, Radu Saghin, Zhihong Xia

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

22 Citas (Scopus)

Resumen

We consider partially hyperbolic diffeomorphisms on compact manifolds. We define the notion of the unstable and stable foliations stably carrying some unique non-trivial homologies. Under this topological assumption, we prove the following two results: if the center foliation is one-dimensional, then the topological entropy is locally a constant; and if the center foliation is two-dimensional, then the topological entropy is continuous on the set of all C diffeomorphisms. The proof uses a topological invariant we introduced, Yomdin's theorem on upper semi-continuity, Katok's theorem on lower semi-continuity for two-dimensional systems, and a refined Pesin-Ruelle inequality we proved for partially hyperbolic diffeomorphisms.

Idioma originalInglés
Páginas (desde-hasta)843-862
Número de páginas20
PublicaciónErgodic Theory and Dynamical Systems
Volumen28
N.º3
DOI
EstadoPublicada - jun. 2008
Publicado de forma externa

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