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Non-Gibbsianness of SRB measures for the natural extension of intermittent systems

Published online by Cambridge University Press:  08 June 2005

MICHIKO YURI
MICHIKO YURI
Affiliation:
Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo 060-0810, Japan (e-mail: yuri@math.sci.hokudai.ac.jp)
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Abstract

For countable-to-one transitive Markov maps, we show that the natural extensions of invariant ergodic weak Gibbs measures absolutely continuous with respect to weak Gibbs conformal measures possess a version of the u-Gibbs property. In particular, if dynamical potentials admit generalized indifferent periodic points then the natural extensions exhibit a non-Gibbsian character in statistical mechanics. Our results can be applicable to certain non-hyperbolic number-theoretical transformations of which natural extensions possess unstable (respectively stable) leaves with subexponential expansion (respectively contraction).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 4 , August 2005 , pp. 1343 - 1356
Copyright
2005 Cambridge University Press

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