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Article Dans Une Revue Commentarii Mathematici Helvetici Année : 2023

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

Résumé

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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hal-04344251 , version 1 (14-12-2023)

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Sébastien Alvarez, Pablo Barrientos, Dmitry Filimonov, Victor Kleptsyn, Dominique Malicet, et al.. Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, II: Applications. Commentarii Mathematici Helvetici, 2023, 98 (4), pp.643-691. ⟨10.4171/cmh/562⟩. ⟨hal-04344251⟩
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