On the measure of maximal entropy for finite horizon Sinai Billiard maps

a Billiard ? Yakov Sinai

412 NOTICES OF THE AMS VOLUME 51, NUMBER 4 Billiards are dynamical systems. In the simplest case, a “billiard table” is a compact domain Q ⊂ Rd with a piecewise smooth boundary. For a large part of the theory the class of smoothness plays no role. The reader is invited to think about components of the boundary ∂Q as subsets of C∞-submanifolds of codimension 1. The phase space M of the billiard ...

Observational Modeling of the Kolmogorov-Sinai Entropy

In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then   the ergodic properties of relative  semi-dynamical systems are investigated.  Also,  a relative version of Kolmogorov-Sinai theorem  is given. Finally, it is proved  that the relative entropy of a...

Entropy Estimate for Maps on Forests

A 1993 result of J. Llibre, and M. Misiurewicz, (Theorem A [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. Also a 1980 result of L.S. Block, J. Guckenheimer, M. Misiurewicz and L.S. Young (Lemma 1.5 [3]) states that if G is an A-graph of f then h(G) ? h( f ). In this pap...

On Finding the Periodic Orbits of the Sinai Billiard

MIXING RATE IN INFINITE MEASURE FOR Z d -EXTENSION, APPLICATION TO THE PERIODIC SINAI BILLIARD

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