Translation numbers define generators of Fk+→ Homeo+(
- Author(s): Golenishcheva-Kutuzova, T;
- Gorodetski, A;
- Kleptsyn, V;
- Volk, D
- et al.
Published Web Locationhttps://doi.org/10.17323/1609-4514-2014-14-2-290-308
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.