We show that Lyapunov exponent for the Sinai billiard is λ=−2log(R)+C+O(Rlog2R) with C=1−4log2+27/(2π2)⋅ζ(3) where
R is the radius of the circular scatterer. We consider the disk-to-disk-map
of the standard configuration where the disks is centered inside a unit square.Comment: 15 pages LaTeX, 3 (useful) figures available from the autho