Vol. 8, No. 4, 2015

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ISSN: 1944-4184 (e-only)
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Outer billiards and tilings of the hyperbolic plane

Filiz Dogru, Emily M. Fischer and Cristian Mihai Munteanu

Vol. 8 (2015), No. 4, 637–651
Abstract

We present new results regarding the periodicity of outer billiards in the hyperbolic plane around polygonal tables which are tiles in regular two-piece tilings of the hyperbolic plane.

Keywords
hyperbolic billiards, outer billiards, polygonal billiards, symbolic dynamics, tiling, rotation number, crochet
Mathematical Subject Classification 2010
Primary: 37E15
Milestones
Received: 28 May 2014
Accepted: 20 June 2014
Published: 23 June 2015

Communicated by Kenneth S. Berenhaut
Authors
Filiz Dogru
Department of Mathematics
Grand Valley State University
Allendale, MI 49401
United States
Emily M. Fischer
Harvey Mudd College
Claremont, CA 91711
United States
Cristian Mihai Munteanu
Department of Mathematics
Jacobs University Bremen
D-28759 Bremen
Germany