On the continuity of topological entropy of certain partially hyperbolic diffeomorphisms

Author:

Wu Weisheng

Abstract

Abstract In this paper, we consider certain partially hyperbolic diffeomorphisms (PHDs) with centre of arbitrary dimension and obtain continuity properties of the topological entropy under C 1 perturbations. The systems considered have subexponential growth in the centre direction and uniform exponential growth along the unstable foliation. Our result applies to PHDs which are Lyapunov stable in the centre direction. It applies to another important class of systems which do have subexponential growth in the centre direction, for which we develop a technique to use exponential mixing property of the systems to get uniform distribution of unstable manifolds. A primary example are the translations on homogeneous spaces which may have centre of arbitrary dimension and of polynomial orbit growth.

Funder

National Natural Science Foundation of China

Fundamental Research Funds for the Central Universities

Publisher

IOP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Reference54 articles.

1. Anomalous partially hyperbolic diffeomorphisms II: stably ergodic examples;Bonatti;Invent. Math.,2016

2. Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent examples;Bonatti;Ann. Sci. École Norm. Sup.,2016

3. Transitive partially hyperbolic diffeomorphisms on 3-manifolds;Bonatti;Topology,2005

4. Transitive partially hyperbolic diffeomorphisms with one-dimensional neutral centre;Bonatti,2019

5. Entropy for group endomorphisms and homogeneous spaces;Bowen;Trans. Am. Math. Soc.,1971

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