Vol. 5, No. 1, 2012

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Trapping light rays aperiodically with mirrors

Zachary Mitchell, Gregory Simon and Xueying Zhao

Vol. 5 (2012), No. 1, 9–14
Abstract

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
Mathematical Subject Classification 2000
Primary: 37D50, 78A05
Milestones
Received: 4 May 2010
Revised: 25 June 2011
Accepted: 6 July 2011
Published: 28 April 2012

Communicated by Joseph O'Rourke
Authors
Zachary Mitchell
Department of Mathematics
Hope College
Holland, MI 49423
United States
Gregory Simon
Department of Mathematics
University of California
Santa Cruz, Santa Cruz, CA 95064
United States
Xueying Zhao
Department of Mathematics
Mount Holyoke College
South Hadley, MA 01075
United States