Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, II: Applications

2021/04/07 by Alvarez, Sébastien, Barrientos, Pablo G., Filimonov, Dmitry +4
#20E06 (Primary) 20E08 #37B05 #37C85 #37E10 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2104.03348

Abstract

In the first part of this work we have established an efficient method to obtain a topological classification of locally discrete, finitely generated, virtually free subgroups of real-analytic circle diffeomorphisms. In this second part we describe several consequences, among which the solution (within this setting) to an old conjecture by P. R. Dippolito [Ann. Math. 107 (1978), 403-453] that actions with invariant Cantor sets must be semi-conjugate to piecewise linear actions. In addition, we exhibit examples of locally discrete, minimal actions which are not of Fuchsian type.

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