Robust Criterion for the Existence of Nonhyperbolic Ergodic Measures

Abstract : We give explicit C (1)-open conditions that ensure that a diffeomorphism possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the existence of a partially hyperbolic compact set with one-dimensional center and positive topological entropy on which the center Lyapunov exponent vanishes uniformly. The conditions of the criterion are met on a C (1)-dense and open subset of the set of diffeomorphisms having a robust cycle. As a corollary, there exists a C (1)-open and dense subset of the set of non-Anosov robustly transitive diffeomorphisms consisting of systems with nonhyperbolic ergodic measures with positive entropy. The criterion is based on a notion of a blender defined dynamically in terms of strict invariance of a family of discs.
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Article dans une revue
Communications in Mathematical Physics, Springer Verlag, 2016, 344 (3), pp. 751-795 〈http://link.springer.com/article/10.1007/s00220-016-2644-5〉. 〈10.1007/s00220-016-2644-5 〉
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01407967
Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 2 décembre 2016 - 18:17:23
Dernière modification le : mercredi 8 février 2017 - 01:04:44

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Jairo Bochi, Christian Bonatti, Lorenzo J. Díaz. Robust Criterion for the Existence of Nonhyperbolic Ergodic Measures. Communications in Mathematical Physics, Springer Verlag, 2016, 344 (3), pp. 751-795 〈http://link.springer.com/article/10.1007/s00220-016-2644-5〉. 〈10.1007/s00220-016-2644-5 〉. 〈hal-01407967〉

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