Journal of Statistical Physics

, Volume 88, Issue 1–2, pp 1–29

Entropy, Lyapunov exponents, and mean free path for billiards

  • N. Chernov

DOI: 10.1007/BF02508462

Cite this article as:
Chernov, N. J Stat Phys (1997) 88: 1. doi:10.1007/BF02508462


We review known results and derive some new ones about the mean free path, Kolmogorov-Sinai entropy, and Lyapunov exponents for billiard-type dynamical systems. We focus on exact and asymptotic formulas for these quantities. The dynamical systems covered in this paper include the priodic Lorentz gas, the stadium and its modifications, and the gas of hard balls. Some open questions and numerical observations are discussed.

Key words

Billiards hard balls Lorentz gas entropy mean free path Lyapunov exponents 

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • N. Chernov
    • 1
  1. 1.Department of MathematicsUniversity of Alabama at BirminghamBirmingham

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