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

Per Dahlqvist
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Abstract

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

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Per Dahlqvist. 1996-01-11. The Lyapunov exponent in the Sinai billiard in the small scatterer limit. https://doi.org/10.1088/0951-7715%2F10%2F1%2F011

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