On the fixed-point proportion of self-similar groups

2025/02/28 by Fariña-Asategui, Jorge, Radi, Santiago · 4 citations
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2503.00185

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 have the same property. The proof uses the approach of Rafe Jones in [15] based on martingales and a recent result of the first author on the dynamics of self-similar groups [6].

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