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Title: Perfect retroreflectors and billiard dynamics
Author: Bachurin, P.
Khanin, K.
Marklof, J.
Plakhov, A.
Keywords: Billiards
Circle Rotation
Dynamical Renormalization
Homogeneous Flow
Issue Date: 2011
Abstract: 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. © 2011 AIMSciences.
Peer review: yes
DOI: 10.3934/jmd.2011.5.33
ISSN: 1930-5311
Appears in Collections:CIDMA - Artigos
OGTCG - Artigos

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