On the fixed-point proportion of self-similar groups
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866929736170602496 |
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| author | Fariña-Asategui, Jorge Radi, Santiago |
| author_facet | Fariña-Asategui, Jorge Radi, Santiago |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00185 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the fixed-point proportion of self-similar groups Fariña-Asategui, Jorge Radi, Santiago Group Theory 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]. |
| title | On the fixed-point proportion of self-similar groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2503.00185 |