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Regular and Chaotic Dynamics, 2003, Volume 8, Issue 1, Pages 83–95
DOI: https://doi.org/10.1070/RD2003v008n01ABEH000227 (Mi rcd767) 		 
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
Citations (2)
DOI: https://doi.org/10.1070/RD2003v008n01ABEH000227
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
Bibliographic databases:
Document Type: Article
MSC: 37E99
Language: English
Citation: R. L. Bishop, “Circular Billiard Tables, Conjugate Loci, and a Cardioid”, Regul. Chaotic Dyn., 8:1 (2003), 83–95
Citation in format AMSBIB
\Bibitem{Bis03}
\by R. L. Bishop
\paper Circular Billiard Tables, Conjugate Loci, and a Cardioid
\jour Regul. Chaotic Dyn.
\yr 2003
\vol 8
\issue 1
\pages 83--95
\mathnet{http://mi.mathnet.ru/rcd767}
\crossref{https://doi.org/10.1070/RD2003v008n01ABEH000227}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1963970}
\zmath{https://zbmath.org/?q=an:1023.37020}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2003RCD.....8...83B}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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