The Lyapunov exponent in the Sinai billiard in the small scatterer limit

الأصل · EN

We show that Lyapunov exponent for the Sinai billiard is λ= -2(R)+C+O(R² R) with C=1-4 2+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.