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

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

1996-01-11

arxiv.org/abs/chao-dyn/9601007v1

Nonlinear Sciences

Chaotic Dynamics

15 pages LaTeX, 3 (useful) figures available from the author

Scientific paper

10.1088/0951-7715/10/1/011

We show that Lyapunov exponent for the Sinai billiard is $\lambda =
-2\log(R)+C+O(R\log^2 R)$ with $C=1-4\log 2+27/(2\pi^2)\cdot \zeta(3)$ 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.

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