English

Random actions of homeomorphisms of Cantor sets embedded in a line and Tits alternative

Dynamical Systems 2024-06-25 v2 Group Theory Geometric Topology

Abstract

In 2000, Margulis proved that any group of homeomorphisms of the circle either preserves a probabilty measure on the circle or contains a free subgroup in two generators, which is reminiscent of the Tits alternatve for linear groups. In this article, we prove an analogous statement for groups of locally monotonic homeomorphisms of a compact subset of R.

Keywords

Cite

@article{arxiv.2304.08070,
  title  = {Random actions of homeomorphisms of Cantor sets embedded in a line and Tits alternative},
  author = {Dominique Malicet and Emmanuel Militon},
  journal= {arXiv preprint arXiv:2304.08070},
  year   = {2024}
}