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Hard Ball Systems and Semi-Dispersive Billiards: Hyperbolicity and Ergodicity

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Hard Ball Systems and the Lorentz Gas

Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 101))

Abstract

The purpose of this survey article is two-fold: First, we intend to introduce the reader into the world of several types of semi-dispersive billiards, such as Sinai’s hard sphere systems in tori or rectangular boxes, the Lorentz-gas, stadia (including Bunimovich’s celebrated one), and Wojtkowski’s systems of 1-D falling balls. The second part of the survey deals with some crucial technical aspects of proving full hyperbolicity (nonzero Lyapunov exponents almost everywhere) and ergodicity for such models of statistical mechanics.

Research supported by the Hungarian National Foundation for Scientific Research, grants OTKA-26176 and OTKA-29849.

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Authors
  1. N. Simányi
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Editors and Affiliations

  1. Institute of Mathematics, Budapest University of Technology and Economics, 91, 1521, Budapest, Hungary

    D. Szász

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© 2000 Springer-Verlag Berlin Heidelberg

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Simányi, N. (2000). Hard Ball Systems and Semi-Dispersive Billiards: Hyperbolicity and Ergodicity. In: Szász, D. (eds) Hard Ball Systems and the Lorentz Gas. Encyclopaedia of Mathematical Sciences, vol 101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04062-1_4

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  • DOI: https://doi.org/10.1007/978-3-662-04062-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08711-0

  • Online ISBN: 978-3-662-04062-1

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