PING-PONG PARTITIONS AND LOCALLY DISCRETE GROUPS OF REAL-ANALYTIC CIRCLE DIFFEOMORPHISMS, I: CONSTRUCTION

Abstract : 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.
Complete list of metadatas

Cited literature [52 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02153478
Contributor : Michele Triestino <>
Submitted on : Wednesday, June 12, 2019 - 11:39:41 AM
Last modification on : Tuesday, June 18, 2019 - 1:34:02 AM

File

Markov_partition-part1-v10.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02153478, version 1
  • ARXIV : 1906.03578

Citation

Juan Alonso, Sébastien Alvarez, Dominique Malicet, Carlos Meniño, Michele Triestino. PING-PONG PARTITIONS AND LOCALLY DISCRETE GROUPS OF REAL-ANALYTIC CIRCLE DIFFEOMORPHISMS, I: CONSTRUCTION. 2019. ⟨hal-02153478⟩

Share

Metrics

Record views

13

Files downloads

16