Correlation decay via coupling for billiards
We consider hyperbolic systems with general singularities
including chaotic billiards. In order to uncover the fact that
hyperbolicity overcomes the fragmentation by singularities, we obtain
the Growth lemma under weaker assumptions than previously adopted
in similar studies. Furthermore, proper measures were coupled whenever
both images under the map simultaneously attracted to a "magnet".
Our approach allows us to obtain the exponential decay of correlations
for a larger class of billiards.