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Quantifying intermittency in the open drivebelt billiard

By Carl P. Dettmann and Orestis Georgiou

Abstract

A "drivebelt" stadium billiard with boundary consisting of circular arcs of differing radius connected by their common tangents shares many properties with the conventional "straight" stadium, including hyperbolicity and mixing, as well as intermittency due to marginally unstable periodic orbits (MUPOs). Interestingly, the roles of the straight and curved sides are reversed. Here we discuss intermittent properties of the chaotic trajectories from the point of view of escape through a hole in the billiard, giving the exact leading order coefficient $\lim_{t\to\infty} t P(t)$ of the survival probability $P(t)$ which is algebraic for fixed hole size. However, in the natural scaling limit of small hole size inversely proportional to time, the decay remains exponential. The big distinction between the straight and drivebelt stadia is that in the drivebelt case there are multiple families of MUPOs leading to qualitatively new effects. A further difference is that most marginal periodic orbits in this system are oblique to the boundary, thus permitting applications that utilise total internal reflection such as microlasers.Comment: 10 pages, 9 figure

Topics: Nonlinear Sciences - Chaotic Dynamics, Mathematics - Dynamical Systems
Publisher: 'AIP Publishing'
Year: 2011
DOI identifier: 10.1063/1.3685522
OAI identifier: oai:arXiv.org:1111.7124

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