Article Dans Une Revue Proceedings of the London Mathematical Society Année : 2022

Symplectomorphisms with positive metric entropy

Résumé

We obtain a dichotomy for $C^1$-generic symplectomorphisms: either all the Lyapunov exponents of almost every point vanish, or the map is partially hyperbolic and ergodic with respect to volume. This completes a program first put forth by Ricardo Ma\~n\'e. A main ingredient in our proof is a generalization to partially hyperbolic invariant sets of the main result in [Dolgopyat-Wilkinson] that stable accessibility is $C^1$ dense among partially hyperbolic diffeomorphisms.

Dates et versions

hal-02367523 , version 1 (18-11-2019)

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Citer

Artur Avila, Sylvain Crovisier, Amie Wilkinson. Symplectomorphisms with positive metric entropy. Proceedings of the London Mathematical Society, 2022, 124, pp.691-712. ⟨10.1112/plms.12437⟩. ⟨hal-02367523⟩
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