Ya. B. Vorobets, G. A. Gal'perin, A. M. Stepin, “Periodic billiard trajectories in polygons: generating mechanisms”, Russian Math. Surveys, 47:3 (1992), 5

Loading [MathJax]/jax/output/SVG/config.js

Russian Mathematical Surveys

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
	Find

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

Russian Mathematical Surveys, 1992, Volume 47, Issue 3, Pages 5–80
DOI: https://doi.org/10.1070/RM1992v047n03ABEH000893 (Mi rm4511)

This article is cited in 38 scientific papers (total in 38 papers)

Periodic billiard trajectories in polygons: generating mechanisms

Ya. B. Vorobets, G. A. Gal'perin, A. M. Stepin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

English version PDF (3761 kB) Citations (38) Russian version article

References:

PDF

HTML

DOI: https://doi.org/10.1070/RM1992v047n03ABEH000893

Received: 24.01.1992

Bibliographic databases:

Document Type: Article

UDC: 517.938+517.987

MSC: 51E12, 52Bxx, 37D50

Language: English

Original paper language: Russian

Citation: Ya. B. Vorobets, G. A. Gal'perin, A. M. Stepin, “Periodic billiard trajectories in polygons: generating mechanisms”, Russian Math. Surveys, 47:3 (1992), 5–80

Citation in format AMSBIB

\Bibitem{VorGalSte92}

\by Ya.~B.~Vorobets, G.~A.~Gal'perin, A.~M.~Stepin

\paper Periodic billiard trajectories in polygons: generating mechanisms

\jour Russian Math. Surveys

\yr 1992

\vol 47

\issue 3

\pages 5--80

\mathnet{http://mi.mathnet.ru/eng/rm4511}

\crossref{https://doi.org/10.1070/RM1992v047n03ABEH000893}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1185299}

\zmath{https://zbmath.org/?q=an:0777.58031}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1992RuMaS..47....5V}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992KU98000002}

Linking options:

https://www.mathnet.ru/eng/rm4511

https://doi.org/10.1070/RM1992v047n03ABEH000893

https://www.mathnet.ru/eng/rm/v47/i3/p9

This publication is cited in the following 38 articles:

Konstantinos Georgiou, Somnath Kundu, Paweł Prałat, Lecture Notes in Computer Science, 14310, Stabilization, Safety, and Security of Distributed Systems, 2023, 157
Matthew Nicol, Karl Petersen, Encyclopedia of Complexity and Systems Science Series, Ergodic Theory, 2023, 3
Matthew Nicol, Karl Petersen, Encyclopedia of Complexity and Systems Science, 2022, 1
Hamid Hezari, Z. Lu, J. Rowlett, “The Dirichlet isospectral problem for trapezoids”, Journal of Mathematical Physics, 62:5 (2021)
A. N. Kirillov, R. V. Alkin, “Ustoichivost periodicheskikh bilyardnykh traektorii v treugolnike”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 18:1 (2018), 25–39
Adolfo Guillot, Lecture Notes in Mathematics, 2204, Geometrical Themes Inspired by the N-body Problem, 2018, 1
Lapidus M.L., Miller R.L., Niemeyer R.G., “Nontrivial paths and periodic orbits of the T -fractal billiard table”, Nonlinearity, 29:7 (2016), 2145–2172
Gianluigi Del Magno, João Lopes Dias, Pedro Duarte, José Pedro Gaivão, Diogo Pinheiro, Springer Proceedings in Mathematics & Statistics, 180, Difference Equations, Discrete Dynamical Systems and Applications, 2016, 179
W.P.atrick Hooper, “The invariant measures of some infinite interval exchange maps”, Geom. Topol, 19:4 (2015), 1895
J.P.. Chen, R.G.. Niemeyer, “Periodic billiard orbits of self-similar Sierpiński carpets”, Journal of Mathematical Analysis and Applications, 2014
Naeem Alkoumi, Felix Schlenk, “Shortest closed billiard orbits on convex tables”, manuscripta math, 2014
I. A. Kotelnikov, S. S. Popov, M. Romé, “Photon neutralizer as an example of an open billiard”, Phys. Rev. E, 87:1 (2013)
Robert G. Niemeyer, Michel L. Lapidus, “Sequences of compatible periodic hybrid orbits of prefractal Koch snowflake billiards”, DCDS-A, 33:8 (2013), 3719
Eugene Gutkin, “Billiard dynamics: An updated survey with the emphasis on open problems”, Chaos, 22:2 (2012), 026116
Matthew Nicol, Karl Petersen, Mathematics of Complexity and Dynamical Systems, 2012, 264
E. A. Gutkin, “Dinamika billiarda: obzornaya statya s aktsentom na nereshennye zadachi”, Nelineinaya dinam., 7:3 (2011), 489–512
A. V. Borisov, A. A. Kilin, I. S. Mamaev, “K modeli negolonomnogo bilyarda”, Nelineinaya dinam., 6:2 (2010), 373–385
Lapidus M.L., Niemeyer R.G., “Towards the Koch Snowflake Fractal Billiard: Computer Experiments and Mathematical Conjectures”, Gems in Experimental Mathematics, Contemporary Mathematics, 517, 2010, 231–263
Matthew Nicol, Karl Petersen, Encyclopedia of Complexity and Systems Science, 2009, 2956
Andrew M. Baxter, Ronald Umble, “Periodic Orbits for Billiards on an Equilateral Triangle”, The American Mathematical Monthly, 115:6 (2008), 479

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	1513
Russian version PDF:	923
English version PDF:	82
References:	116
First page:	3

Что такое QR-код?

Registration to the website

Logotypes