10 papers
Proportion of periodic points in reduction of polynomials
Santiago Radi
In 2014, Juul, Kurlberg, Madhu and Tucker asked the following: given a number field and a rational function with coefficients in , if denotes the reduct…
Branch iterated Galois groups with positive fixed-point proportion and positive Hausdorff dimension
Santiago Radi
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…
Corrigendum and addendum to "Fixed-point-free elements of iterated monodromy groups" [Trans. of the American Mathematical Society Vol. 367, No. 3 (2015), 2023-2049]
Jorge Fariña-Asategui, Rafe Jones, Santiago Radi
In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.
Fixed-point proportion of geometric iterated Galois groups
Jorge Fariña-Asategui, Santiago Radi
In 1980, Odoni initiated the study of the fixed-point proportion of iterated Galois groups of polynomials motivated by prime density problems in arithmetic dynamics. The main goal…
Groups of finite type: classification and structural properties
Santiago Radi
Groups of finite type (also called finitely constrained groups), introduced by Grigorchuk, are known to be the closure of regular branch groups. This article explores many of their…
Random subgroups of branch groups
Jorge Fariña-Asategui, Santiago Radi
We show that independent Haar-random elements in a super strongly fractal branch profinite group generate a free subgroup acting freely on the boundary of the tree. This improves a…