Statistical Properties of SRB Measures in Billiards
by
Nikolai Chernov
University of Alabama at Birmingham

We discuss various billiard models for which statistical properties have been investigated recently. The main result is exponential decay of correlations for planar periodic Lorentz gases, with and without horizon, and for planar dispersing billiards with corner points. For Lorentz gases under expernal forces, an SRB invariant measure is constructed. we prove its uniqueness and Bernoulli property, as well as exponential decay of correlations. For some other billiard models, the research is underway, and partial results are available.

Date received: March 4, 2000