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arXiv · 1408.4252

Diffeomorphisms with positive metric entropy

Artur Avila·Sylvain Crovisier·Amie Wilkinson
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Abstract

We obtain a dichotomy for $C^1$-generic, volume-preserving diffeomorphisms: either all the Lyapunov exponents of almost every point vanish or the volume is ergodic and non-uniformly Anosov (i.e. nonuniformly hyperbolic and the splitting into stable and unstable spaces is dominated). This completes a program first put forth by Ricardo Ma\~n\'e.

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Artur Avila, Sylvain Crovisier, Amie Wilkinson. 2014-08-19. Diffeomorphisms with positive metric entropy. https://arxiv.org/abs/1408.4252

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