## Locally discrete expanding groups of analytic diffeomorphisms of the circle.(English)Zbl 1455.37029

Summary: We show that a finitely subgroup of $$\operatorname{Diff}^\omega(\mathbf{S}^1)$$ that is expanding and locally discrete in the analytic category is analytically conjugated to a uniform lattice in $$\widetilde{\mathrm{PGL}}_2^k(\mathbf{R})$$ acting on the $$k$$th covering of $$\mathbf{R}P^1$$ for a certain integer $$k>0$$.

### MSC:

 37C85 Dynamics induced by group actions other than $$\mathbb{Z}$$ and $$\mathbb{R}$$, and $$\mathbb{C}$$ 37E10 Dynamical systems involving maps of the circle 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 37D25 Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms

### Keywords:

analytical conjugation; expanding map; map of the circle
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