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This article is cited in 4 scientific papers (total in 4 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.
Received: June 23, 2013; in revised form October 2, 2013
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
Linking options:
https://www.mathnet.ru/eng/mmj523 https://www.mathnet.ru/eng/mmj/v14/i2/p291
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Abstract page: | 662 | References: | 57 |
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