Chaotic scattering from pinball machine like systems

Abstract

We study a model inspired by the pinball machine involving chaotic scattering of particles on hard disks with inelasticity. This system exhibits sensitivity not only on the initial conditions of the scattering point particle but also on the external force produced by the pinballs. The deflection function shows fractal structure with regions of wild oscillations which are exponentially compressed as a function of the force exerted by the hard disks. The chaotic properties of the repeller, such as the scaling of the fractal dimension, the Lyapunov exponents and the pressure function, are studied for different geometric configurations.