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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Dimension of hyperbolic measures of random diffeomorphisms


Authors: Pei-Dong Liu and Jian-Sheng Xie
Journal: Trans. Amer. Math. Soc. 358 (2006), 3751-3780
MSC (2000): Primary 37C45; Secondary 37H15
DOI: https://doi.org/10.1090/S0002-9947-06-03933-X
Published electronically: April 11, 2006
MathSciNet review: 2218998
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Abstract: We consider dynamics of compositions of stationary random $ C^2$ diffeomorphisms. We will prove that the sample measures of an ergodic hyperbolic invariant measure of the system are exact dimensional. This is an extension to random diffeomorphisms of the main result of Barreira, Pesin and Schmeling (1999), which proves the Eckmann-Ruelle dimension conjecture for a deterministic diffeomorphism.


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Additional Information

Pei-Dong Liu
Affiliation: School of Mathematical Sciences, Peking University, 100871 Beijing, People’s Republic of China
Email: lpd@pku.edu.cn

Jian-Sheng Xie
Affiliation: School of Mathematical Sciences, Peking University, 100871 Beijing, People’s Republic of China
Address at time of publication: Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100080 Beijing, People’s Republic of China
Email: js_xie@yahoo.com.cn

DOI: https://doi.org/10.1090/S0002-9947-06-03933-X
Keywords: Random dynamical systems, Eckmann-Ruelle conjecture, hyperbolic measure
Received by editor(s): January 16, 2004
Received by editor(s) in revised form: April 11, 2004
Published electronically: April 11, 2006
Additional Notes: This work was supported by the 973 Fund of China for Nonlinear Science and the NSFDYS
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.