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Translation numbers define generators of Fk+→ Homeo+(

  • Author(s): Golenishcheva-Kutuzova, T
  • Gorodetski, A
  • Kleptsyn, V
  • Volk, D
  • et al.

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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