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stable ergodicity

Ergodic Theory and Dynamical Systems (1)

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On the stable ergodicity of Berger–Carrasco’s example
Part of
DAVI OBATA
Journal:

Ergodic Theory and Dynamical Systems / Volume 40 / Issue 4 / April 2020

Published online by Cambridge University Press:

27 September 2018, pp. 1008-1056

Print publication:

April 2020
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We prove the stable ergodicity of an example of a volume-preserving, partially hyperbolic diffeomorphism introduced by Berger and Carrasco in [Berger and Carrasco. Non-uniformly hyperbolic diffeomorphisms derived from the standard map. Comm. Math. Phys.329 (2014), 239–262]. This example is robustly non-uniformly hyperbolic, with a 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.