Regular and Chaotic Dynamics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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)
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}
Linking options:
  • https://www.mathnet.ru/eng/rcd767
  • https://www.mathnet.ru/eng/rcd/v8/i1/p83
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:69
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024