The probabilistic method is a technique for proving combinatorial existence results by
means of showing that a randomly chosen object has the desired properties with positive …

This book is meant as a complement to our monograph Cellular Automata and Groups,
Springer Monographs in Mathematics, 2010 [CAG]. It consists of more than 600 fully solved …

A generalization of the simulation theorem for semidirect products Page 1 Ergod. Th. & Dynam.
Sys. (2019), 39, 3185–3206 doi:10.1017/etds.2018.21 c Cambridge University Press, 2018 A …

We say that a finitely generated group $\Gamma $ is (dynamically) self-simulable if every
effectively closed action of $\Gamma $ on a closed subset of $\{\mathtt {0},\mathtt …

We look at constructions of aperiodic subshifts of finite type (SFTs) on fundamental groups of
graph of groups. In particular, we prove that all generalized Baumslag-Solitar groups (GBS) …

In this paper we study the combinatorics of free Borel actions of the group $\mathbb Z^ d $
on Polish spaces. Building upon recent work by Chandgotia and Meyerovitch, we introduce …

Let $ G $ be a group and $ H\leqslant G $ a subgroup. The free extension of an $ H $-
subshift $ X $ to $ G $ is the $ G $-subshift $\widetilde {X} $ whose configurations are those …

We show that every effectively closed action of a finitely generated group $ G $ on a closed
subset of $\{0, 1\}^{\mathbb {N}} $ can be obtained as a topological factor of the $ G …

We study uniformly recurrent subgroups (URS) introduced by Glasner and Weiss [18].
Answering their query we show that any URS Z of a finitely generated group is the stability …

In this article we study the centralizer of a minimal aperiodic action of a countable group on
the Cantor set (an aperiodic minimal Cantor system). We show that any countable residually …