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Particle drift in self-similar billiards

Published online by Cambridge University Press:  01 April 2008

N. CHERNOV and
D. DOLGOPYAT
N. CHERNOV
Affiliation:
Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA (email: chernov@math.uab.edu)
D. DOLGOPYAT
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA (email: dmitry@math.umd.edu)
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Abstract

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We study a particle moving at unit speed in a channel made by connected self-similar billiard tables that grow in size by a factor r>1 from left to right (this model was recently introduced in the physics literature by Barra, Gilbert and Romo). Let q(T) denote the position of the particle at time T. Our main result is the existence of an asymptotic distribution of q(T)/T as $T\to \infty $ and {ln T/ln r}→ρ for some 0≤ρ<1.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 2: William Parry Memorial Volume , April 2008, pp. 389 - 403
Copyright
Copyright © Cambridge University Press 2008

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