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

DOI:
https://doi.org/10.1090/S0002-9939-2011-10985-7

Published electronically:
July 29, 2011

MathSciNet review:
2869114

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Abstract | References | Similar Articles | Additional Information

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

Email:
krerley@gmail.com

DOI:
https://doi.org/10.1090/S0002-9939-2011-10985-7

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.