Related papers: Shift limits of a non-autonomous system
Let $G$ be a countable monoid and let $A$ be an Artinian group (resp. an Artinian module). Let $\Sigma \subset A^G$ be a closed subshift which is also a subgroup (resp. a submodule) of $A^G$. Suppose that $\Gamma$ is a finitely generated…
We show that on the four-symbol full shift, there is a finitely generated subgroup of the automorphism group whose action is (set-theoretically) transitive of all orders on the points of finite support, up to the necessary caveats due to…
This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…
Following the work of Louisa and Michael Barnsley on results in tops of iterated function systems, we extend their work to graph-directed iterated function systems by investigating the relationship between top addresses and shift spaces.…
We study limit sets of stable cellular automata standing from a symbolic dynamics point of view where they are a special case of sofic shifts admitting a steady epimorphism. We prove that there exists a right-closing almost-everywhere…
A topological space $A$ is said to be compatible with a set $\Sigma$ of equations (involving operation symbols $F_t$) iff there are continuous operations $\overline F_t$ identically satisfying $\Sigma$ on $A$. The paper's main focus is on…
A finite family $\mathcal{F}=\{f_1,\ldots,f_n\}$ of continuous selfmaps of a given metric space $X$ is called an iterated function system (shortly IFS). In a case of contractive selfmaps of a complete metric space is well-known that IFS has…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
Invertible fermionic topological (IFT) phases are gapped phases of matter with nondegenerate ground states on any closed spatial manifold. When open boundary conditions are imposed, nontrivial IFT phases support gapless boundary degrees of…
It has been recently shown that, under appropriate hypotheses, the $\omega$-limit sets of a dynamical system are characterized by internal chain transitivity. In this paper, we examine generalizations of these ideas in the context of the…
The aim of this article is to find appropriate definitions for shifts of finite type and sofic shifts in a general context of symbolic dynamics. We start showing that the classical definitions of shifts of finite type and sofic shifts, as…
In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the…
A featured transition system is a transition system in which the transitions are annotated with feature expressions: Boolean expressions on a finite number of given features. Depending on its feature expression, each individual transition…
In this work, we investigate the dynamics of a general non-autonomous system generated by a commutative family of homeomorphisms. In particular, we investigate properties such as periodicity, equicontinuity, minimality and transitivity for…
We utilize the topological holographic framework to characterize and gain insights into the nature of quantum critical points and gapless phases in fermionic quantum systems. Topological holography is a general framework that describes the…
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…
Let $\Delta\subsetneq\V$ be a proper subset of the vertices $\V$ of the defining graph of an irreducible and aperiodic shift of finite type $(\Sigma_{A}^{+},\S)$. Let $\Sigma_{\Delta}$ be the subshift of allowable paths in the graph of…
An interval translation map (ITM) is a map $T \colon I \to I$ defined as a piecewise translation on a finite partition of an interval $I$ into $r \ge 2$ subintervals. Unlike classical interval exchange transformations (IETs), the images of…
This paper is a technical continuation of ``Natural Axiom Schemata Extending ZFC. Truth in the Universe?'' In that paper we argue that $CIFS$ is a natural axiom schema for the universe of sets. In particular it is a natural closure…
The occurrence of tracking or tipping situations for a transition equation $x'=f(t,x,\Gamma(t,x))$ is analyzed under the assumptions on concavity in $x$ either of the maps giving rise to the asymptotic equations $x'=f(t,x,\Gamma_\pm(t,x))$…