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DIFFRACTIVE GEODESICS OF A POLYGONAL BILLIARD

Published online by Cambridge University Press:  02 February 2006

Luc Hillairet
Luc Hillairet
Affiliation:
UMPA ENS-Lyon, 46 allée d’Italie, 69364 Lyon Cedex 7, France ([email protected])
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Abstract

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We define the notion of diffractive geodesic for a polygonal billiard or, more generally, for a Euclidean surface with conical singularities. We study the local geometry of the set of such geodesics of given length and we relate it to a number that we call classical complexity. This classical complexity is then computed for any diffractive geodesic. As an application we describe the set of periodic diffractive geodesics as well as the symplectic aspects of the ‘diffracted flow’.

Keywords

Primary 37D50polygonal billiarddiffractive orbitsconical singularities
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 1 , February 2006 , pp. 71 - 86
Copyright
Copyright © Edinburgh Mathematical Society 2006