Related papers: Broken family sensitivity in transitive systems

A quasi one--dimensional system of trapped, repulsively interacting atoms (e.g., an ion chain) exhibits a structural phase transition from a linear chain to a zigzag structure, tuned by reducing the transverse trap potential or increasing…

A family of maps or flows depending on a parameter $\nu$ which varies in an interval, spans a certain property if along the interval this property depends continuously on the parameter and achieves some asymptotic values along it. We…

Given two positive integers $n\geq 3$ and $t\leq n$, the permutations $\sigma,\pi \in \operatorname{Sym}(n)$ are $t$-setwise intersecting if they agree (setwise) on a $t$-subset of $\{1,2,\ldots,n\}$. A family $\mathcal{F} \subset…

A family $\mathcal{A}$ of sets is said to be \emph{$t$-intersecting} if any two sets in $\mathcal{A}$ have at least $t$ common elements. A central problem in extremal set theory is to determine the size or structure of a largest…

A topological space $X$ is called a topological fractal if $X=\bigcup_{f\in\mathcal F}f(X)$ for a finite system $\mathcal F$ of continuous self-maps of $X$, which is topologically contracting in the sense that for every open cover $\mathcal…

A continuum $X$ is a dendrite if it is locally connected and contains no simple closed curve, a self mapping $f$ of $X$ is called monotone if the preimage of any connected subset of $X$ is connected. If $X$ is a dendrite and $f:X\to X$ is a…

We show that a system of hard discs confined to a narrow channel exhibits a fragile-strong fluid crossover located at the maximum of the isobaric heat capacity and that the relaxation times for different channel widths fall onto a single…

This paper addresses the problem of designing a {\em fault-tolerant} $(\alpha, \beta)$ approximate BFS structure (or {\em FT-ABFS structure} for short), namely, a subgraph $H$ of the network $G$ such that subsequent to the failure of some…

We state that for continuous interval maps the existence of a non empty closed invariant subset which is transitive and sensitive to initial conditions is implied by positive topological entropy and implies chaos in the sense of Li-Yorke,…

This article is devoted to study which conditions imply that a topological dynamical system is mean sensitive and which do not. Among other things we show that every uniquely ergodic, mixing system with positive entropy is mean sensitive.…

A set $A$ $t$-intersects a set $B$ if $A$ and $B$ have at least $t$ common elements. Families $\mathcal{A}_1, \mathcal{A}_2, \dots, \mathcal{A}_k$ of sets are cross-$t$-intersecting if, for every $i$ and $j$ in $\{1, 2, \dots, k\}$ with $i…

In a recent breakthrough, Adiprasito, Avvakumov, and Karasev constructed a triangulation of the $n$-dimensional real projective space with a subexponential number of vertices. They reduced the problem to finding a small downward closed…

In data transmission networks, the availability of data transmission is equivalent to the existence of the fractional factor of the corresponding graph which is generated by the network. Research on the existence of fractional factors under…

A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\rightarrow u_2\rightarrow \cdots \rightarrow u_t$, $t \geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\rightarrow u_j$…

We investigate the ferromagnetic-glassy transitions which separate the low-temperature ferromagnetic and spin-glass phases in the temperature-disorder phase diagram of three-dimensional Ising spin-glass models. For this purpose, we consider…

In this paper we study $F$-divided bundles on irreducible Noetherian normal $F$-finite $\mathbb{F}_p$-schemes and we show that their Tannakian category is governed by the behaviour at the generic point. In particular, if $U\subset X$ is an…

The Kibble-Zurek mechanism constitutes one of the most fascinating and universal phenomena in the physics of critical systems. It describes the formation of domains and the spontaneous nucleation of topological defects when a system is…

The low-temperature kinetics of the strongly correlated electron liquid inhabiting a solid is analyzed. It is demonstrated that a softly damped branch of transverse zero sound emerges when several bands cross the Fermi surface…

Sensitive boundary condition dependence (BCD) is reported in a convectively unstable system with noise, where the amplitude of generated oscillatory dynamics in the downstream depends sensitively on the boundary value. This BCD is explained…

The article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map $f\times f^2 \times...\times f^m$, where $f\colon X\ra X$ is a topological dynamical system on a…