Billiards with polynomial mixing rates

Abstract

While many dynamical systems of mechanical origin, in particular billiards,\nare strongly chaotic -- enjoy exponential mixing, the rates of mixing in many\nother models are slow (algebraic, or polynomial). The dynamics in the latter\nare intermittent between regular and chaotic, which makes them particularly\ninteresting in physical studies. However, mathematical methods for the analysis\nof systems with slow mixing rates were developed just recently and are still\ndifficult to apply to realistic models. Here we reduce those methods to a\npractical scheme that allows us to obtain a nearly optimal bound on mixing\nrates. We demonstrate how the method works by applying it to several classes of\nchaotic billiards with slow mixing as well as discuss a few examples where the\nmethod, in its present form, fails.\n