Every expanding measure has the nonuniform specification property

Details Every expanding measure has the nonuniform specification property Every expanding measure has the nonuniform specification property

2010-07-08

arxiv.org/abs/1007.1449v1

Mathematics

Dynamical Systems

10 pages

Scientific paper

Exploring abundance and non lacunarity 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 lenght of almost every dynamical ball. In particular, we conclude that any ergodic measure with positive Lyapunov exponents satisfy 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 limit of Dirac measures on periodic points.

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