Billiards in ideal  hyperbolic polygons

Simon Castle; Norbert Peyerimhoff; Karl Friedrich Siburg

doi:10.3934/dcds.2011.29.893

Article Contents

2011, Volume 29, Issue 3: 893-908. Doi: 10.3934/dcds.2011.29.893

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Billiards in ideal hyperbolic polygons

1.
Department of Math. Sciences, Durham University, Durham DH1 3LE
2.
Technische Universität Dortmund, Fakultät für Mathematik, 44221 Dortmund

Received: October 31, 2009

Revised: May 31, 2010

Published: August 2011

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Abstract

We consider billiard trajectories in ideal hyperbolic polygons and present a conjecture about the minimality of the average length of cyclically related billiard trajectories in regular hyperbolic polygons. We prove this conjecture in particular cases, using geometric and algebraic methods from hyperbolic geometry.

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Mathematics Subject Classification: Primary: 37D40, 53A35; Secondary: 37C27.

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