RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2019, Volume 210, Number 3, Pages 17–74 (Mi msb9041)  

This article is cited in 3 scientific papers (total in 3 papers)

The Fomenko–Zieschang invariants of nonconvex topological billiards

V. V. Vedyushkina

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: Along with a classical planar billiard, one can consider a topological billiard for which the motion takes place on a locally planar surface obtained by an isometric gluing of several planar domains along boundaries that are arcs of confocal quadrics. Here, a point is moving inside every domain along segments of straight lines, passing from one domain into another when it hits the boundary of the gluing. The author has previously obtained the Liouville classification of all such topological billiards obtained by gluings along convex boundaries. In the present paper, we classify all topological integrable billiards obtained by gluing both along convex and along nonconvex boundaries from elementary billiards bounded by arcs of confocal quadrics. For all such nonconvex topological billiards, the Fomenko–Zieschang invariants (marked molecules $W^*$) of Liouville equivalence are calculated.
Bibliography: 25 titles.

Keywords: integrable system, billiard, Liouville equivalence, Fomenko–Zieschang invariant.

Funding Agency Grant Number
Russian Science Foundation 17-11-01303
This work was supported by the Russian Science Foundation (project no. 17-11-01303).


DOI: https://doi.org/10.4213/sm9041

Full text: PDF file (2279 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2019, 210:3, 310–363

Bibliographic databases:

UDC: 517.938.5
MSC: Primary 37J35; Secondary 37G10, 70E40
Received: 20.11.2017

Citation: V. V. Vedyushkina, “The Fomenko–Zieschang invariants of nonconvex topological billiards”, Mat. Sb., 210:3 (2019), 17–74; Sb. Math., 210:3 (2019), 310–363

Citation in format AMSBIB
\Bibitem{Ved19}
\by V.~V.~Vedyushkina
\paper The Fomenko--Zieschang invariants of nonconvex topological billiards
\jour Mat. Sb.
\yr 2019
\vol 210
\issue 3
\pages 17--74
\mathnet{http://mi.mathnet.ru/msb9041}
\crossref{https://doi.org/10.4213/sm9041}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2019SbMat.210..310V}
\elib{http://elibrary.ru/item.asp?id=37089813}
\transl
\jour Sb. Math.
\yr 2019
\vol 210
\issue 3
\pages 310--363
\crossref{https://doi.org/10.1070/SM9041}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000468092700002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85068316526}


Linking options:
  • http://mi.mathnet.ru/eng/msb9041
  • https://doi.org/10.4213/sm9041
  • http://mi.mathnet.ru/eng/msb/v210/i3/p17

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. A. T. Fomenko, V. V. Vedyushkina, “Billiards and integrability in geometry and physics. New scope and new potential”, Moscow University Mathematics Bulletin, 74:3 (2019), 98–107  mathnet  crossref  mathscinet  isi
    2. V. V. Vedyushkina (Fokicheva), A. T. Fomenko, “Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards”, Izv. Math., 83:6 (2019), 1137–1173  mathnet  crossref  crossref  adsnasa  isi
    3. V. V. Vedyushkina, “Integriruemye billiardy realizuyut toricheskie sloeniya na linzovykh prostranstvakh i 3-tore”, Matem. sb., 211:2 (2020), 46–73  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:173
    References:20
    First page:9

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020