Abstract
Bunimovich billiards are ergodic and mixing. However, if the billiard table contains very large arcs on its boundary then if there exist trajectories experience infinitely many collisions in the vicinity of periodic trajectories on the large arc. The hyperbolicity is nonuniform and the mixing rate is very slow. The corresponding dynamics are intermittent between regular and chaotic, which makes them particularly interesting in physical studies. The study of mixing rates in intermittent chaotic systems is more difficult than that of truly chaotic ones, and the resulting estimates may depend on delicate details of the dynamics in the traps. We present a rigorous analysis of the corresponding singularities and correlations to certain class of billiards and show the mixing rate is of order 1/n.
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Schedule a callMore From: Acta Mathematicae Applicatae Sinica, English Series
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