99-422 Fernando J. Sanchez-Salas

Horseshoes with infinitely many branches and a characterization of Sinai-Ruelle-Bowen measures (798K, .ps .dvi) Nov 9, 99

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Abstract. Let $f$ be a $C^2$ diffeomorphism of a compact riemannian manifold $M^m$ and $\mu$ an ergodic f-invariant Borel probability with non zero Lyapunov exponents. We prove that $\mu$ is a Sinai-Ruelle-Bowen (SRB) measure if and only if we can reduce the dynamics on an invariant set of total measure to a horseshoe with infinitely many branches and variable return times. Also, and as a consequence of our approach we give a new proof of the well known Ledrappier-Young's characterization theorem.

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