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Article Dans Une Revue Journal of Combinatorial Algebra Année : 2023

Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction

Résumé

Following the recent advances in the study of groups of circle diffeomorphisms, we classify the topological dynamics of locally discrete, finitely generated, virtually free subgroups of the group Diff^ω_+(S^1) of orientation preserving real-analytic circle diffeomorphisms, which include all subgroups of Diff^ω_+(S^1) acting with an invariant Cantor set. An important tool that we develop, of independent interest, is the extension of classical ping-pong lemma to actions of fundamental groups of graphs of groups. Our main motivation is an old conjecture by P.R. Dippolito [Ann. Math. 107 (1978), 403-453] from foliation theory, which we solve in this restricted but significant setting: this and other consequences of the classification will be treated in more detail in a companion work.
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hal-02153478 , version 1 (12-06-2019)

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Juan Alonso, Sébastien Alvarez, Dominique Malicet, Carlos Meniño Cotón, Michele Triestino. Ping-pong partitions and locally discrete groups of real-analytic circle diffeomorphisms, I: Construction. Journal of Combinatorial Algebra, 2023, ⟨10.4171/jca/78⟩. ⟨hal-02153478⟩
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