07-124 A.Rapoport and Rom-Kedar, V.
Chaotic scattering by steep potentials (7602K, pdf) May 21, 07
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Abstract. The singular billiard limit of smooth steep scattering potentials is utilized as a skeleton for studying the properties of the scattering problem; It is shown that for one class of chaotic scatterers, named here regular Sinai scatterers, the scattering properties of the smooth system limit to those of the billiard. On the other hand, it is shown that for other chaotic scatterers, that belong to the class of singular Sinai scatterers (scatterers with singular bounded semi-orbits), the fractal dimension of the scattering function of the smooth flow may be controlled, for arbitrary steep potentials, by changing the ratio between the steepness parameter and a parameter which controls the billiards' geometry.

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