1 citations · 1 across the 8 of their papers we have counts for
10 papers
Spectrum of the basilica group and the associated real and complex 2D dynamics
Eric Bedford, Rostislav Grigorchuk, Nguyen-Bac Dang +1
In this paper, we study the iteration over the real and complex loci of a specific rational map, found by Grigorchuk and Zuk. This two dimensional map arises as the renormalization…
Branch actions and the structure lattice
Jorge Fariña-Asategui, Rostislav Grigorchuk
J. S. Wilson proved in 1971 an isomorphism between the structural lattice associated to a group belonging to his second class of groups with every proper quotient finite and the Bo…
SFT covers for actions of the first Grigorchuk group
Rostislav Grigorchuk, Ville Salo
We study symbolic dynamical representations of actions of the first Grigorchuk group , namely its action on the boundary of the infinite rooted binary tree, its representation i…
On maximal subgroups of ample groups
Rostislav Grigorchuk, Yaroslav Vorobets
The paper is concerned with maximal subgroups of the ample (better known as topological full) groups of homeomorphisms of totally disconnected compact metrizable topological spaces…
On the structure of finitely generated subgroups of branch groups
Dominik Francoeur, Rostislav Grigorchuk, Paul-Henry Leemann +1
We describe the block structure of finitely generated subgroups of branch groups with the so-called subgroup induction property, including the first Grigorchuk group …
Characters and IRS's on branch groups and embeddings into hyperfinite factor
Artem Dudko, Rostislav Grigorchuk
Using the construction by Bencs and Tóth of invariant random subgroups on weakly branch groups acting on regular rooted trees we produce uncountably many indecomposable characters…
On Mealy-Moore coding and images of Markov measures
Rostislav Grigorchuk, Roman Kogan, Yaroslav Vorobets
We study the images of the Markov measures under transformations generated by the Mealy automata. We find conditions under which the image measure is absolutely continuous or singu…
Finitely generated subgroups of branch groups and subdirect products of just infinite groups
Rostistlav Grigorchuk, Paul-Henry Leemann, Tatiana Nagnibeda
The aim of this paper is to describe the structure of the finitely generated subgroups of a family of branch groups, which includes the first Grigorchuk group and the Gupta-Sidki 3…
Asymptotic aspects of Schreier graphs and Hanoi Towers groups
Rostislav Grigorchuk, Zoran Sunik
We present relations between growth, growth of diameters and the rate of vanishing of the spectral gap in Schreier graphs of automaton groups. In particular, we introduce a series…
Branch Groups
Laurent Bartholdi, Rostislav I. Grigorchuk, Zoran Sunik
This is a long introduction to the theory of "branch groups": groups acting on rooted trees which exhibit some self-similarity features in their lattice of subgroups.