K-mixing for aperiodic Lorentz gases

Abstract

We prove a general theorem on the decomposition into K-mixing components for recurrent, piecewise-smooth hyperbolic maps in two dimensions. In contrast with classical results, we do not assume that the map preserves a probability measure. As an application, we show that every recurrent aperiodic Lorentz gas satisfying certain uniformity assumptions is K-mixing. Finally, we discuss some consequences of K-mixing for the decay of correlations relative to zero-mean $L^1$ observables in aperiodic Lorentz gases.

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