On the Stable Ergodicity of Berger-Carrasco's example

2018/02/19 by Davi Obata, Obata, Davi
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1802.06570

openalex publication_date 2018/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the stable ergodicity of an example of a volume-preserving, partially hyperbolic diffeomorphism introduced by Pierre Berger and Pablo Carrasco. This example is robustly non-uniformly hyperbolic, with two dimensional center, almost every point has both positive and negative Lyapunov exponents along the center direction and does not admit a dominated splitting of the center direction. The main novelty of our proof is that we do not use accessibility.

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