Nikolai Chernov, Hongkun Zhang
Billiards with polynomial mixing rates
(712K, Postscript)

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