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arXiv · 2104.03348

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

Sébastien Alvarez·Pablo G. Barrientos·Dmitry Filimonov·Victor Kleptsyn·Dominique Malicet·Carlos Meniño·Michele Triestino
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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.

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Sébastien Alvarez, Pablo G. Barrientos, Dmitry Filimonov, Victor Kleptsyn, Dominique Malicet, Carlos Meniño, Michele Triestino. 2021-04-07. Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, II: Applications. https://arxiv.org/abs/2104.03348

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