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

Anton Gorodetski; Denis Volk; Tatiana Golenishcheva-Kutuzova; Victor Kleptsyn

arxiv: 1306.5522 · v1 · pith:YGQBHXCFnew · submitted 2013-06-24 · 🧮 math.DS · math.GR

Translation numbers define generators of F_k^+to {rm Homeo_+}(mathbb{S}¹)

Tatiana Golenishcheva-Kutuzova , Anton Gorodetski , Victor Kleptsyn , Denis Volk This is my paper

classification 🧮 math.DS math.GR

keywords circlegeneratorshomeomorphismsnumberstranslationactionantonovchange

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We consider a minimal action of a finitely generated semigroup by homeomorphisms of a 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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Translation numbers define generators of F_k^+to {rm Homeo_+}(mathbb{S}¹)

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