Related papers: Lamplighters admit weakly aperiodic SFTs

We consider the structure of aperiodic points in $\mathbb Z^2$-subshifts, and in particular the positions at which they fail to be periodic. We prove that if a $\mathbb Z^2$-subshift contains points whose smallest period is arbitrarily…

The action of a finite group $G$ on a subshift of finite type $X$ is called free, if every point has trivial stabilizer, and it is called inert, if the induced action on the dimension group of $X$ is trivial. We show that any two free inert…

Building on work from Sun and Kechris-Quorning, we prove that every acylindrically hyperbolic group $G$ admits a weakly mixing probability measure preserving action $G \curvearrowright (X,\mathcal{B},\mu)$ which is faithful but not…

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 for which the restriction to every coset of $H$ is a configuration from…

In this paper we study the directions of periodicity of three-dimensional subshifts of finite type (SFTs) and in particular their slopes. A configuration of a subshift has a slope of periodicity if it is periodic in exactly one direction,…

We prove that if every Schmidt subgroup of a group $G$ is subnormal or modular, then $G/F(G)$ is cyclic

Let $S=\{s_i\in\mathbb N\cup\{0\}:0\leq s_i<s_{i+1}\}$ and let $d_{0}=s_{0}$ and $\Delta(S)=\{d_{n}\}_{n}$ where $d_{n}=s_{n}-s_{n-1}$. In this note, we show that an $S$-gap shift is subshift of finite type (SFT) if and only if $S$ is…

$\lambda$-graph systems are labeled Bratteli diagram with shift operations. They present subshifts. Their matrix presentations are called symbolic matrix systems. We define skew products of $\lambda$-graph systems and study extensions of…

We show that the image of a subshift $X$ under various injective morphisms of symbolic algebraic varieties over monoid universes with algebraic variety alphabets is a subshift of finite type, resp. a sofic subshift, if and only if so is…

Let $\Gamma$ be an undirected and simple graph. A set $ S $ of vertices in $\Gamma$ is called a {cyclic vertex cutset} of $\Gamma$ if $\Gamma - S$ is disconnected and has at least two components each containing a cycle. If $\Gamma$ has a…

A group $G$ given by a presentation $G = < \mathcal A \| \mathcal R >$ is called weakly finitely presented if every finitely generated subgroup of $G$, generated by (images of) some words in $\mathcal A^{\pm 1}$, is naturally isomorphic to…

The main result of this paper (Theorem B) asserts that under natural conditions, any weakly-split Tits system in G(k), G a reductive or quasi-reductive group over an arbitrary field k, is the standard one.

A subgroup $R$ of a finite group $G$ is weakly subnormal in $G$ if $R$ is not subnormal in $G$ but it is subnormal in every proper overgroup of $R$ in $G$. In this paper, we first classify all finite groups $G$ which contains a weakly…

Shifts of finite type and the notion of shadowing, or pseudo-orbit tracing, are powerful tools in the study of dynamical systems. In this paper we prove that there is a deep and fundamental relationship between these two concepts. Let $X$…

Let $G=\left\langle S|R_{A}\right\rangle $ be a semigroup with generating set $ S$ and equivalences $R_{A}$ among $S$ determined by a matrix $A$. This paper investigates the complexity of $G$-shift spaces by yielding the topological…

Given a group G, we consider its classifying space for the family of virtually cyclic subgroups. We show for many groups, including for example, one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and CAT(0) cube groups,…

For any subshift, define $F_X(n)$ to be the collection of distinct follower sets of words of length $n$ in $X$. Based on a similar result of the second and third authors, we conjecture that if there exists an $n$ for which $|F_X(n)| \leq…

Let $X$ be a real or complex Banach space and $T_t:X\to X$ is a power bounded operator (or a $C_0$-semigroup). If there exists a "occasionally" attracting compact subset K (for each x$ in unit ball $\liminf_n \rho(T^n x, K)=0$ then there…

It has been recently proved that the automorphism group of a minimal subshift with non-superlinear word complexity is virtually $\mathbb{Z}$ [DDPM15, CK15]. In this article we extend this result to a broader class proving that the…

It is well known that \omega-limit sets are internally chain transitive and have weak incompressibility; the converse is not generally true, in either case. However, it has been shown that a set is weakly incompressible if and only if it is…