Work

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

Year: 2026

Type: article

Abstract: In 2000, Margulis proved that any group of homeomorphisms of the circle either preserves a probability measure on the circle or contains a free subgroup on two generators, which is reminiscent of the Tits alternative for linear groups. In this article, we prove an analogous statement for groups of locally monotonic homeomorphisms of a compact subset of ℝ . The proof relies on dynamical properties of random walks on the group, which may be of independent interest.

Source: Annales Henri Lebesgue

DOI: 10.5802/ahl.259

Authors: Dominique Malicet, Emmanuel Militon

Institutions: Laboratoire d’Analyse et de Mathématiques Appliquées, Université Gustave Eiffel, Université Côte d'Azur, Laboratoire Jean-Alexandre Dieudonné

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Agence Nationale de la Recherche, Centre National de la Recherche Scientifique

Awards: G3010527862, Groups of homeomorphisms of manifolds