A FAMILY OF CHAOTIC BILLIARDS WITH VARIABLE MIXING RATES

Abstract

We describe a one-parameter family of dispersing (hence hyperbolic, ergodic and mixing) billiards where the correlation function of the collision map decays as 1/n a (here n denotes the discrete time), in which the degree a ∈ (1, ∞) changes continuously with the parameter of the family, β. We also derive an explicit relation between the degree a and the family parameter β.