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Trapping light
rays aperiodically with mirrors
Zachary Mitchell, Gregory Simon and Xueying Zhao
Vol. 5 (2012), No. 1, 9–14
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Abstract |
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We construct a configuration of disjoint segment mirrors in the plane that traps a single light ray aperiodically, providing a negative solution to a conjecture of O’Rourke and Petrovici. We expand this to show that any finite number of rays from a source can be trapped aperiodically. |
Keywords
trapping light, mirrors, billiards, dynamical systems
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Mathematical Subject Classification 2000
Primary: 37D50, 78A05
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Milestones
Received: 4 May 2010
Revised: 25 June 2011
Accepted: 6 July 2011
Published: 28 April 2012
Communicated by Joseph O'Rourke
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Authors |
| Zachary Mitchell | |
| Department of Mathematics Hope College Holland, MI 49423 United States |
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| Gregory Simon | |
| Department of Mathematics University of California Santa Cruz, Santa Cruz, CA 95064 United States |
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| Xueying Zhao | |
| Department of Mathematics Mount Holyoke College South Hadley, MA 01075 United States |
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