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arXiv · 2503.00185

On the fixed-point proportion of self-similar groups

Jorge Fariña-Asategui·Santiago Radi
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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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Jorge Fariña-Asategui, Santiago Radi. 2025-02-28. On the fixed-point proportion of self-similar groups. https://doi.org/10.1112/blms.70368

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