Let G be a countable residually finite group (for instance, endowed with the Haar measure.
The construction we propose is general (for amenable and non-amenable residually finite …

Using tools from computable analysis we develop a notion of effectiveness for general
dynamical systems as those group actions on arbitrary spaces that contain a computable …

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) …

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 …

Subshifts are colorings of $\mathbb {Z}^ d $ defined by families of forbidden patterns. Given
a subshift and a finite pattern, its extender set is the set of admissible completions of this …

A subshift of finite type is a set of tilings of a group subject to a finite number of local
constraints, where the group acts by translation. In recent years, much progress has been …

We study symbolic dynamical representations of actions of the first Grigorchuk group $ G $,
namely its action on the boundary of the infinite rooted binary tree, its representation in the …

We provide an example of a non-finitely generated group which admits a nonempty strongly
aperiodic subshift of finite type. Furthermore, we completely characterize the groups with this …

The Medvedev degree of a subshift is a dynamical invariant of computable origin that can be
used to compare the complexity of subshifts that contain only uncomputable configurations …

We study the problem of realizing families of subgroups as the set of stabilizers of
configurations from a subshift of finite type (SFT). This problem generalizes both the …