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Proceedings of the American Mathematical Society

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Expansive measures versus Lyapunov exponents

Authors: Alma Armijo and Maria José Pacifico
Journal: Proc. Amer. Math. Soc. 146 (2018), 3895-3906
MSC (2010): Primary 37C40
Published electronically: June 1, 2018
MathSciNet review: 3825843
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Abstract: In this paper we investigate the relation between measure-expansiveness and hyperbolicity. We prove that non-atomic invariant ergodic measures with all of their Lyapunov exponents positive are positively measure-expansive. We also prove that local diffeomorphisms robustly positively measure-expansive are expanding. Finally, we prove that a $ C^1$-volume-preserving diffeomorphism that cannot be accumulated by positively measure-expansive diffeomorphisms has a dominated splitting.

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Additional Information

Alma Armijo
Affiliation: Departamento de Matemática, Universidad de las Américas and Universidad de Santiago de Chile, Santiago, Chile

Maria José Pacifico
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil

Received by editor(s): February 7, 2017
Received by editor(s) in revised form: September 5, 2017, October 10, 2017, and November 26, 2017
Published electronically: June 1, 2018
Additional Notes: This work was partially supported by CAPES, CNPq, FAPERJ
Communicated by: Nimish Shah
Article copyright: © Copyright 2018 American Mathematical Society