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Thermodynamic formalism for certain nonhyperbolic maps

Published online by Cambridge University Press:  01 October 1999

MICHIKO YURI
MICHIKO YURI
Affiliation:
Department of Business Administration, Sapporo University, Nishioka, Toyohira-ku, Sapporo 062, Japan
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Abstract

We establish a generalized thermodynamic formalism for certain nonhyperbolic maps with countably many preimages. We study existence and uniqueness of conformal measures and statistical properties of the equilibrium states absolutely continuous with respect to the conformal measures. We will see that such measures are not Gibbs but satisfy a version of Gibbs property (weak Gibbs measure). We apply our results to a one-parameter family of one-dimensional maps and a two-dimensional nonconformal map related to number theory. Both of them admit indifferent periodic points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 5 , October 1999 , pp. 1365 - 1378
Copyright
1999 Cambridge University Press

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