Fractal properties of scattering singularities

Abstract

The authors discuss properties of the set of scattering singularities in regions of irregular scattering. The authors show how a symbolic organisation of the set can be used to determine the fractal dimension and the scaling function. These yields information on the distribution of Lyapunov exponents of bounded orbits. The specific model studied is the motion of a particle in a plane, elastically reflected by three circular discs centred on the corners of an equilateral triangle.