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Following recent work of Chernov, Markarian, and Zhang, it is known that thebilliard map for dispersing billiards with zero angle cusps has slow decay ofcorrelations with rate 1/n. Since the collisions inside a cusp occur in quicksuccession, it is reasonable to expect a much faster decay rate in continuoustime. In this paper we prove that the flow is rapid mixing: correlations decayfaster than any polynomial rate. A consequence is that the flow admits strongstatistical properties such as the almost sure invariance principle, eventhough the billiard map does not.  The techniques in this paper yield new results for other standard examples inplanar billiards, including Bunimovich flowers and stadia.

Decay of correlations and invariance principles for dispersing billiards with cusps, and related planar billiard flows