Chernov N.
Entropy, Lyapunov exponents and mean free path for billiards
(71K, LATEX)
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.