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A note on Sinaï and Bunimovich's Markov partition for billiards (1986)

Lévy, Yves-Emmanuel

Springer

Journal of statistical physics 45 (1986), S. 63-68

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ISSN: 1572-9613

Keywords: Billiards ; Markov partition ; Markov process ; dynamical system with singularity ; hyperbolic mapping

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01033077

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