Dimension of hyperbolic measures of random diffeomorphisms
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- by Pei-Dong Liu and Jian-Sheng Xie PDF
- Trans. Amer. Math. Soc. 358 (2006), 3751-3780 Request permission
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.References
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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
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2218998