On the weaker forms of the specification property and their applications

Yamamoto, Kenichiro

doi:10.1090/S0002-9939-09-09937-7

On the weaker forms of the specification property and their applications
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Proc. Amer. Math. Soc. 137 (2009), 3807-3814 Request permission

Abstract:

We show the following two results, which are derived from the weaker forms of the specification property: Firstly, if an automorphism of a compact metric abelian group with finite topological entropy is ergodic under the Haar measure, then it satisfies the level 2 large deviation principle. Secondly, the topological pressure formula for periodic orbits is given under the expansiveness and the almost product property.

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