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, 2020, Volume 25, Issue 1, Pages 11–17
DOI: https://doi.org/10.1134/S1560354720010037 (Mi rcd1046) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Special issue: In honor of Valery Kozlov for his 70th birthday

Two Variations on the Periscope Theorem

Serge Tabachnikov

Department of Mathematics, Penn State University, University Park, PA 16802, USA
Citations (2)
References:
PDF
HTML
DOI: https://doi.org/10.1134/S1560354720010037
Abstract: A (multidimensional) spherical periscope is a system of two ideal mirrors that reflect every ray of light emanating from some point back to this point. A spherical periscope defines a local diffeomorphism of the space of rays through this point, and we describe such diffeomorphisms. We also solve a similar problem for (multidimensional) reversed periscopes, the systems of two mirrors that reverse the direction of a parallel beam of light.
Keywords: periscope, optical reflection, projectively gradient vector field.
Funding agency Grant number
National Science Foundation DMS-1510055
This work was supported by NSF grant DMS-1510055.
Received: 22.08.2019
Accepted: 24.12.2019
Bibliographic databases:
Document Type: Article
MSC: 78A05, 37D50
Language: English
Citation: Serge Tabachnikov, “Two Variations on the Periscope Theorem”, Regul. Chaotic Dyn., 25:1 (2020), 11–17
Citation in format AMSBIB
\Bibitem{Tab20}
\by Serge Tabachnikov
\paper Two Variations on the Periscope Theorem
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 1
\pages 11--17
\mathnet{http://mi.mathnet.ru/rcd1046}
\crossref{https://doi.org/10.1134/S1560354720010037}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000515001300002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85079800306}
Linking options:
  • https://www.mathnet.ru/eng/rcd1046
  • https://www.mathnet.ru/eng/rcd/v25/i1/p11
    • 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:166
    References:77
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024