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This article is cited in 2 scientific papers (total in 2 papers)
Dynamics of billiards
Circular Billiard Tables, Conjugate Loci, and a Cardioid
R. L. Bishop University of Illinois at Urbana-Champaign,
1409 W. Green St., Urbana, Illinois 61801
Abstract:
Some of the major concepts of Riemannian geometry are explained in terms of billiards on a circular billiard table: conjugate loci, exponential map, Morse theory on the path space. The conjugate loci are related to the caustics of classical optics of a circular reflector. The change in form of those conjugate loci and caustics as the source point moves is classified and illustrated with many pictures based on numerical data.
Received: 16.02.2003
Citation:
R. L. Bishop, “Circular Billiard Tables, Conjugate Loci, and a Cardioid”, Regul. Chaotic Dyn., 8:1 (2003), 83–95
Linking options:
https://www.mathnet.ru/eng/rcd767 https://www.mathnet.ru/eng/rcd/v8/i1/p83
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Abstract page: | 55 |
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