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Translation numbers define generators of f-k(+) -> Homeo(+) (S-1)
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2014 (English)In: Moscow Mathematical Journal, ISSN 1609-3321, Vol. 14, no 2, 291-308 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2014. Vol. 14, no 2, 291-308 p.
Keyword [en]
Groups of homeomorphisms of the circle, rotation number, translation number, synchronization
National Category
URN: urn:nbn:se:kth:diva-155501ISI: 000342789300006OAI: diva2:762097

QC 20141110

Available from: 2014-11-10 Created: 2014-11-06 Last updated: 2014-11-10Bibliographically approved

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Volk, Denis
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