On the fixed‐point proportion of self‐similar groups
Abstract
Abstract We prove that super strongly fractal groups acting on regular rooted trees have null fixed‐point proportion. In particular, we show that the fixed‐point proportion of an infinite family of iterated monodromy groups of exceptional complex polynomials has the same property. The proof uses the approach of Rafe Jones based on martingales and a recent result of the first author on the dynamics of self‐similar groups.
Fields of Study & Subjects
advanced mathematical theories
Mathematical Dynamics and Fractals
Advanced Topology and Set Theory
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 7
- Publication date
- 1 July 2026
- Language
- EN