A note on Sina� and Bunimovich's Markov partition for billiards

Abstract

I present a construction of Markov partitions related to a statistical description of a class of hyperbolic dynamical systems of ℝ2 with singularities, through a general algorithm. This construction, correct, in contrast to previous attempts, applies in particular to billiards problems, yielding an easy-to-handle Markov partition; as an application, the incorrectness of a lemma of Bunimovich and Sinai (which was known to need improvement) is made clear.