Hyperbolic measures with transverse intersections of stable and unstable manifolds

Michihiro Hirayama; Naoya Sumi

doi:10.3934/dcds.2013.33.1451

Article Contents

2013, Volume 33, Issue 4: 1451-1476. Doi: 10.3934/dcds.2013.33.1451

This issue Previous Article Glauber dynamics in continuum: A constructive approach to evolution of states Next Article Dynamics of $\lambda$-continued fractions and $\beta$-shifts

Hyperbolic measures with transverse intersections of stable and unstable manifolds

Michihiro Hirayama^1, and
Naoya Sumi^2,

1.
Faculty of Engineering, Kyushu Institute of Technology, Tobata, Fukuoka 804-8550
2.
Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551

Received: December 31, 2010

Revised: August 31, 2012

Published: March 2013

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Abstract

Let $f$ be a diffeomorphism of a manifold preserving a hyperbolic Borel probability measure $ μ $ having transverse intersections for almost every pair of stable and unstable manifolds. A lower bound on the Hausdorff dimension of generic sets is given in terms of the Lyapunov exponents and the metric entropy. Furthermore we obtain a lower bound for the large deviation rate.

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Mathematics Subject Classification: 37A50, 37C40, 37C45, 37D25.

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