The conformal geometry of billiards
Author:
Laura DeMarco
Journal:
Bull. Amer. Math. Soc. 48 (2011), 33-52
MSC (2010):
Primary 37D50, 32G15
DOI:
https://doi.org/10.1090/S0273-0979-2010-01322-7
Published electronically:
October 15, 2010
MathSciNet review:
2738905
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: This article provides an introduction to some recent results in billiard dynamics. We present results that follow from a study of compact Riemann surfaces (equipped with a holomorphic 1-form) and an $\mathrm {SL}_2\mathbb {R}$ action on the moduli spaces of these surfaces. We concentrate on the progress toward classification of “optimal” billiard tables, those with the simplest trajectory structure.
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Additional Information
Laura DeMarco
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago
MR Author ID:
677013
Email:
demarco@math.uic.edu
Received by editor(s):
July 19, 2010
Published electronically:
October 15, 2010
Article copyright:
© Copyright 2010
American Mathematical Society