Related papers: On images of sofic systems

Let (X,T) be a topologically transitive dynamical system. We show that if there is a subsystem (Y,T) of (X,T) such that (X\times Y, T\times T) is transitive, then (X,T) is strongly chaotic in the sense of Li and Yorke. We then show that…

Let $\varphi\in C^0 \cap W^{1,2}(\Sigma, X)$ where $\Sigma$ is a compact Riemann surface, $X$ is a compact locally CAT(1) space, and $W^{1,2}(\Sigma,X)$ is defined as in Korevaar-Schoen. We use the technique of harmonic replacement to prove…

We find (completeness type) conditions on topological semilattices $X,Y$ guaranteeing that each continuous homomorphism $h:X\to Y$ has closed image $h(X)$ in $Y$.

We establish necessary and sufficient conditions for a dynamical system to be topologically conjugate to the Morse minimal set, the shift orbit closure of the Morse sequence, and conditions for topological conjugacy to the closely related…

We prove a generalization of Krieger's embedding theorem, in the spirit of zero-error information theory. Specifically, given a mixing shift of finite type $X$, a mixing sofic shift $Y$, and a surjective sliding block code $\pi: X \to Y$,…

We define the notion of {\em classifying space} of a topological stack and show that every topological stack \X has a classifying space X which is a topological space well-defined up to weak homotopy equivalence. Under a certain…

We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…

We show that finite-type surfaces are characterized by a topological analog of the Hopf property. Namely, an oriented surface $\Sigma$ is of finite-type if and only if every proper map $f\colon\Sigma\to \Sigma$ of degree one is homotopic to…

Let $Y\to X$ be a finite normal cover of a wedge of $n\geq 3$ circles. We prove that for any $v\neq 0\in H_1(Y;\mathbb{Q})$ there exists a lift $\widetilde{F}$ to $Y$ of a homotopy equivalence $F:X\to X$ so that the set of iterates…

We study metric versions of transitivity, mixing, and hypercyclicity for continuous maps, based on intersections of the form \( f^{n}(U)\cap B_{\delta}(V)\neq\varnothing. \) We introduce $\delta$-topological transitivity,…

In the framework of a recently proposed topological approach to phase transitions, some sufficient conditions ensuring the presence of the spontaneous breaking of a Z_2 symmetry and of a symmetry-breaking phase transition are introduced and…

The topological classification of gapped band structures depends on the particular definition of topological equivalence. For translation-invariant systems, stable equivalence is defined by a lack of restrictions on the numbers of occupied…

Given a countable sofic group $\Gamma$, a finite alphabet $A$, a subshift $X \subseteq A^\Gamma$, and a potential $\phi: X \to \mathbb{R}$, we give sufficient conditions on $X$ and $\phi$ for expressing, in the uniqueness regime, the sofic…

We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety $X$, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification…

For a smooth spacetime $X$, based on the timelike homotopy classes of its timelike paths, we define a topology on $X$ that refines the Alexandrov topology and always coincides with the manifold topology. The space of timelike or causal…

Let $\Gamma$ be a sofic group, $\Sigma$ be a sofic approximation sequence of $\Gamma$ and $X$ be a $\Gamma$-subshift with nonnegative sofic topological entropy with respect to $\Sigma$. Further assume that $X$ is a shift of finite type, or…

In this paper, some characterizations about transitivity, mildly mixing property, $\mathbf{a}$-transitivity, equicontinuity, uniform rigidity and proximality of Zadeh's extensions restricted on some invariant closed subsets of the space of…

We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially…

Let $X$ be a compact metric space and $T:X\longrightarrow X$ be continuous. Let $h^*(T)$ be the supremum of topological sequence entropies of $T$ over all subsequences of $\mathbb Z_+$ and $S(X)$ be the set of the values $h^*(T)$ for all…

Given any strong orbit equivalence class of minimal Cantor systems and any cardinal number that is finite, countable, or the continuum, we show that there exists a minimal subshift within the given class whose number of asymptotic…