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Every expanding measure has the nonuniform specification property

Author: Krerley Oliveira
Journal: Proc. Amer. Math. Soc. 140 (2012), 1309-1320
MSC (2010): Primary 37D25, 37A99
Published electronically: July 29, 2011
MathSciNet review: 2869114
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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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Additional Information

Krerley Oliveira
Affiliation: Instituto de Matemática, Universidade Federal de Alagoas, 57072-090 Maceió, AL, Brazil

Keywords: Periodic points, Lyapunov exponents.
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.