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JMD

We construct semi-infinite billiard domains which reverse the direction of most
incoming particles. We prove that almost all particles will leave the open
billiard domain after a finite number of reflections. Moreover, with high
probability the exit velocity is exactly opposite to the entrance velocity, and
the particle's exit point is arbitrarily close to its initial position. The
method is based on asymptotic analysis of statistics of entrance times to a
small interval for irrational circle rotations. The rescaled entrance times
have a limiting distribution in the limit when the length of the interval
vanishes. The proof of the main results follows from the study of related
limiting distributions and their regularity properties.

keywords:
billiards
,
dynamical renormalization
,
retroreflectors.
,
homogeneous
flow
,
Recurrence
,
circle rotation

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