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This article is cited in 3 scientific papers (total in 3 papers)
Search light in billiard tables
N. Chernova, G. A. Galperinb a Department of Mathematics,
University of Alabama at Birmingham,
Birmingham, AL 35294
b Department of Mathematics,
Eastern Illinois University,
Charleston, IL 61920
Abstract:
We investigate whether a search light, $S$, illuminating a tiny angle ("quot") with vertex $A$ inside a bounded region $Q \in \mathbb{R}^2$ with the mirror boundary $\partial Q$, will eventually illuminate the entire region $Q$. It is assumed that light rays hitting the corners of $Q$ terminate. We prove that: (I) if $Q= a$ circle or an ellipse, then either the entire $Q$ or an annulus between two concentric circles/confocal ellipses (one of which is $\partial Q$) or the region between two confocal hyperbolas will be illuminated; (II) if $Q= a$ square, or (III) if $Q= a$ dispersing (Sinai) or semidespirsing billiards, then the entire region $Q$ is will be illuminated.
Received: 07.04.2003
Citation:
N. Chernov, G. A. Galperin, “Search light in billiard tables”, Regul. Chaotic Dyn., 8:2 (2003), 225–241
Linking options:
https://www.mathnet.ru/eng/rcd779 https://www.mathnet.ru/eng/rcd/v8/i2/p225
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