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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
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