Survival probability for the stadium billiard

CP Dettmann, O Georgiou

Research output: Contribution to journalArticle (Academic Journal)peer-review

31 Citations (Scopus)


We consider the open stadium billiard, consisting of two semicircles joined by parallel straight sides with one hole situated somewhere on one of the sides. Due to the hyperbolic nature of the stadium billiard, the initial decay of trajectories, due to loss through the hole, appears exponential. However, some trajectories (bouncing ball orbits) persist and survive for long times and therefore form the main contribution to the survival probability function at long times. Using both numerical and analytical methods, we concur with previous studies that the long-time survival probability for a reasonably small hole drops like Constant×(time)−1; here we obtain an explicit expression for the Constant.
Translated title of the contributionSurvival probability for the stadium billiard
Original languageEnglish
Pages (from-to)2395 - 24032
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume238, issues 23-24
Publication statusPublished - Dec 2009

Bibliographical note

Publisher: Elsevier

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