Rigidity of the dynamics of ${{\rm Aut}}({\mathsf{F}}_n)$ on representations into a compact group
Dynamical Systems
2026-03-11 v1 Group Theory
Abstract
Let be a compact Lie group. Let be the free group of rank . We describe the orbits of on when is sufficiently large. The dynamics stabilizes: orbit closures and invariant probability measures are algebraic, as in Ratner's theorems.
Cite
@article{arxiv.2603.09456,
title = {Rigidity of the dynamics of ${{\rm Aut}}({\mathsf{F}}_n)$ on representations into a compact group},
author = {Serge Cantat and Christophe Dupont and Florestan Martin-Baillon},
journal= {arXiv preprint arXiv:2603.09456},
year = {2026}
}