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

Deroin, Bertrand

J. Topol. 13, No. 3, 1216-1229 (2020).

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