On Pesin's entropy formula for dominated splittings without mixed behavior

2015/12/28 by Dawei Yang, Yang, Dawei, Yongluo Cao +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Differential Equations and Dynamical Systems #Caveolin-1 and cellular processes #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS

paper · pdf · doi:10.48550/arxiv.1512.08541

arxiv created 2015/12/28 · openalex publication_date 2015/12/28 · arxiv updated 2015/12/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For C¹ diffeomorphisms, we prove that the Pesin's entropy formula holds for some invariant measure supported on any topological attractor that admits a dominated splitting without mixed behavior. We also prove Shub's entropy conjecture for diffeomorphisms having such kind of splittings.

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