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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the weaker forms of the specification property and their applications


Author: Kenichiro Yamamoto
Journal: Proc. Amer. Math. Soc. 137 (2009), 3807-3814
MSC (2000): Primary 37B40; Secondary 60F10
Published electronically: June 10, 2009
MathSciNet review: 2529890
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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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Additional Information

Kenichiro Yamamoto
Affiliation: Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
Email: yamamoto.k.ak@m.titech.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09937-7
PII: S 0002-9939(09)09937-7
Keywords: Specification, large deviation, topological entropy periodic orbit
Received by editor(s): December 25, 2008
Received by editor(s) in revised form: February 23, 2009
Published electronically: June 10, 2009
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.