Some sufficient conditions for transitivity of Anosov diffeomorphisms

2022/03/16 by F. Micena, Micena, F. · 1 citation
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2203.08930

Abstract

Given a C²- Anosov diffemorphism f: M → M, we prove that the jacobian condition Jfⁿ(p) = 1, for every point p such that fⁿ(p) = p, implies transitivity. As application in the celebrated theory of Sinai-Ruelle-Bowen, this result allows us to state a classical theorem of Livsic-Sinai without directly assuming transitivity as a general hypothesis. A special consequence of our result is that every C²-Anosov diffeomorphism, for which every point is regular, is indeed transitive.

Cited by

• Spectral decomposition and entropy for open set-valued maps

Related

• Diffeomorphisms Holder conjugate to Anosov diffeomorphisms
• Unique SRB measures and transitivity for Anosov diffeomorphisms
• A relation between entropy and transitivity of Anosov diffeomorphisms
• On sufficient conditions for the transitivity of homeomorphisms
• Transitivity of Infinite-Dimensional Extensions of Anosov Diffeomorphisms