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Translation Numbers Define Generators of Fk+→Homeo+(

Published Web Location

https://doi.org/10.17323/1609-4514-2014-14-2-290-308
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.

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