Branch iterated Galois groups with positive fixed-point proportion and positive Hausdorff dimension
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910032445046784 |
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| author | Radi, Santiago |
| author_facet | Radi, Santiago |
| contents | In this article we prove that the arithmetic profinite iterated monodromy group of a post-critically infinite unicritical polynomial is regular branch (and so of positive Hausdorff dimension), and has positive fixed-point proportion when the degree is odd. The examples are instances of a bigger family of regular branch groups constructed in this article, whose fixed-point proportion can be computed explicitly and is positive in many cases. This gives the first examples outside the binary rooted tree where a level-transitive group has positive Hausdorff dimension and positive fixed-point proportion, answering in the negative a question of Jones (2008). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Branch iterated Galois groups with positive fixed-point proportion and positive Hausdorff dimension Radi, Santiago Group Theory Number Theory In this article we prove that the arithmetic profinite iterated monodromy group of a post-critically infinite unicritical polynomial is regular branch (and so of positive Hausdorff dimension), and has positive fixed-point proportion when the degree is odd. The examples are instances of a bigger family of regular branch groups constructed in this article, whose fixed-point proportion can be computed explicitly and is positive in many cases. This gives the first examples outside the binary rooted tree where a level-transitive group has positive Hausdorff dimension and positive fixed-point proportion, answering in the negative a question of Jones (2008). |
| title | Branch iterated Galois groups with positive fixed-point proportion and positive Hausdorff dimension |
| topic | Group Theory Number Theory |
| url | https://arxiv.org/abs/2602.13428 |