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Mosc. Math. J., 2014, Volume 14, Number 2, Pages 291–308 (Mi mmj523)  

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

Translation numbers define generators of $F_k^+\to\mathrm{Homeo}_+(\mathbb S^1)$

Tatiana Golenishcheva-Kutuzovaa, Anton Gorodetskib, Victor Kleptsync, Denis Volkde

a Moscow Center for Continuous Mathematical Education, Moscow, Russia
b Department of Mathematics, University of California, Irvine CA 92697, USA
c CNRS, Institute of Mathematical Research of Rennes (IRMAR, UMR 6625 du CNRS), France
d Institute for Information Transmission Problems, Russian Academy of Sciences
e KTH Matematik, Lindstedsvägen 25, SE-100 44 Stockholm Sweden

Abstract: We consider a minimal action of a finitely generated semigroup by homeomorphisms of the circle, and show that the collection of translation numbers of individual elements completely determines the set of generators (up to a common continuous change of coordinates). One of the main tools used in the proof is the synchronization properties of random dynamics of circle homeomorphisms: Antonov's theorem and its corollaries.

Key words and phrases: groups of homeomorphisms of the circle, rotation number, translation number, synchronization.

Full text: http://www.mathjournals.org/.../2014-014-002-006.html
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Bibliographic databases:

Document Type: Article
MSC: 37E10, 37E45, 20M20
Received: June 23, 2013; in revised form October 2, 2013
Language: English

Citation: Tatiana Golenishcheva-Kutuzova, Anton Gorodetski, Victor Kleptsyn, Denis Volk, “Translation numbers define generators of $F_k^+\to\mathrm{Homeo}_+(\mathbb S^1)$”, Mosc. Math. J., 14:2 (2014), 291–308

Citation in format AMSBIB
\Bibitem{GolGorKle14}
\by Tatiana~Golenishcheva-Kutuzova, Anton~Gorodetski, Victor~Kleptsyn, Denis~Volk
\paper Translation numbers define generators of $F_k^+\to\mathrm{Homeo}_+(\mathbb S^1)$
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 2
\pages 291--308
\mathnet{http://mi.mathnet.ru/mmj523}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3236495}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000342789300006}


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    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. Gorodetski, V. Kleptsyn, “Synchronization properties of random piecewise isometries”, Comm. Math. Phys., 345:3 (2016), 781–796  crossref  mathscinet  zmath  isi  scopus
    2. P. G. Barrientos, F. H. Ghane, D. Malicet, A. Sarizadeh, “On the chaos game of iterated function systems”, Topol. Methods Nonlinear Anal., 49:1 (2017), 105–132  crossref  mathscinet  zmath  isi  scopus
    3. K. Gelfert, O. Stenflo, “Random iterations of homeomorphisms on the circle”, Mod. Stoch. Theory Appl., 4:3 (2017), 253–271  crossref  mathscinet  zmath  isi
  • Moscow Mathematical Journal
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