JournalscmhVol. 98, No. 4pp. 643–691

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

  • Sébastien Alvarez

    Universidad de la República, Montevideo, Uruguay

  • Pablo G. Barrientos

    Universidade Federal Fluminense, Rio de Janeiro, Brazil

  • Dmitry Filimonov

    HSE University, Moscow, Russia

  • Victor Kleptsyn

    CNRS, Institut de Récherche Mathématique de Rennes, France

  • Dominique Malicet

    Université Gustave Eiffel, Champs-sur-Marne, France

  • Carlos Meniño Cotón

    CITMAGA; Instituto Investigaciones Tecnológicas, Santiago de Compostela; Universidade de Vigo, Spain

  • Michele Triestino

    Université de Bourgogne, Dijon, France
Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, II: Applications cover
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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.

Cite this article

Sébastien Alvarez, Pablo G. Barrientos, Dmitry Filimonov, Victor Kleptsyn, Dominique Malicet, Carlos Meniño Cotón, Michele Triestino, Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, II: Applications. Comment. Math. Helv. 98 (2023), no. 4, pp. 643–691

DOI 10.4171/CMH/562