97-205 Chernov N.

Entropy, Lyapunov exponents and mean free path for billiards (71K, LATEX) Apr 10, 97

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Abstract. 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 the paper include periodic Lorentz gas, stadium and its modifications, and the gas of hard balls, for which we prove rigorously the classical Boltzmann formula for the intercollision time. Some open questions and numerical observations are discussed.

Files: 97-205.tex