Every expanding measure has the nonuniform specification property
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Abstract:Exploring abundance and nonlacunarity of hyperbolic times for endomorphisms preserving an ergodic probability with positive Lyapunov exponents, we obtain that there are periodic points of period growing sublinearly with respect to the length of almost every dynamical ball. In particular, we conclude that any ergodic measure with positive Lyapunov exponents satisfies the nonuniform specification property. As consequences, we (re)obtain estimates on the recurrence to a ball in terms of the Lyapunov exponents, and we prove that any expanding measure is the limit of Dirac measures on periodic points.
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- Krerley Oliveira
- Affiliation: Instituto de Matemática, Universidade Federal de Alagoas, 57072-090 Maceió, AL, Brazil
- Email: email@example.com
- Received by editor(s): July 28, 2010
- Received by editor(s) in revised form: December 22, 2010, and December 27, 2010
- Published electronically: July 29, 2011
- Additional Notes: This work was partially supported by CNPq, CAPES, FAPEAL, INCTMAT and PRONEX
- Communicated by: Bryna Kra
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 140 (2012), 1309-1320
- MSC (2010): Primary 37D25, 37A99
- DOI: https://doi.org/10.1090/S0002-9939-2011-10985-7
- MathSciNet review: 2869114