Related papers: Transitivity in nonautonomous systems
Let $f \colon X \to X$ be a continuous map on a compact metric space $X$ and let $\alpha_f$, $\omega_f$ and $ICT_f$ denote the set of $\alpha$-limit sets, $\omega$-limit sets and nonempty closed internally chain transitive sets…
In this paper, we provide a new criterion for the stable transitivity of volume preserving finite generated group on any compact Riemannian manifold. As one of our applications, we generalised a result of Dolgopyat and Krikorian in…
We consider a \emph{code} to be a subset of the vertex set of a \emph{Hamming graph}. In this setting a \emph{neighbour} of the code is a vertex which differs in exactly one entry from some codeword. This paper examines codes with the…
Systems that are not smooth can undergo bifurcations that are forbidden in smooth systems. We review some of the phenomena that can occur for piecewise-smooth, continuous maps and flows when a fixed point or an equilibrium collides with a…
In this paper we establish Functional Limit Theorems for the range of random walks in $\mathbb{Z}^d$ that are in the domain of attraction of a non-degenerate $\beta$-stable process in the weakly transient and recurrent regimes. These…
Microreversibility rules the fluctuations of the currents flowing across open systems in nonequilibrium (or equilibrium) steady states. As a consequence, the statistical cumulants of the currents and their response coefficients at arbitrary…
Let $(X,d)$ be a compact metric space, $f:X \mapsto X$ be a continuous map with the specification property, and $\varphi: X \mapsto \IR$ be a continuous function. We prove a variational principle for topological pressure (in the sense of…
In this paper we aim to present two general results regarding, on one hand, the openness stability of set-valued maps and, on the other hand, the metric regularity behavior of the implicit multifunction related to a generalized variational…
The win ratio (WR) is a novel statistic used in randomized controlled trials that can account for hierarchies within event outcomes. In this paper we report and study the long-run non-transitive behavior of the win ratio and the closely…
A continuous map $f$ on a compact metric space $X$ induces in a natural way the map $\tilde f$ on the hyperspace $\mathcal K(X)$ of all closed non-empty subsets of $X$. We study the question of transmission of chaos between $f$ and $\tilde…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
Let $(X,d)$ be a metric space and $f: X \rightarrow X$ be a homeomorphism. We say that a dynamical system $(X,f)$ is \emph{expansive}, with constant of expansivity $c \in \mathbb{R{^+}}$, if for all $x,y \in X$ , $x \neq y$, exists $n \in…
A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…
Noncommutative functions are graded functions between sets of square matrices of all sizes over two vector spaces that respect direct sums and similarities. They possess very strong regularity properties (reminiscent of the regularity…
In this paper, we study some features of n-normed spaces with respect to norms of its quotient spaces. We define continuous functions with respect to the norms of its quotient spaces and show that all types of continuity are equivalent. We…
We consider time-delay systems with a finite number of delays in the state space $L^\infty\times\mathbb{R}^n$. In this framework, we show that forward completeness implies the bounded reachability sets property, while this implication was…
It is investigated the existence of a separately continuous function $f:X\times Y\to \mathbb R$ with an onepoint set of discontinuity for topological spaces $X$ and $Y$ which satisfy compactness type conditions. In particular, it is shown…
We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…
The main purpose is to characterise continuous maps that are $n$-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius $n$-homomorphisms between two function spaces that correspond to…
Non-equilibrium fluctuation theorems (NFTs) relate work performed on a system as its Hamiltonian varies with time, to equilibrium data of the initial and final states. In a classical context the system energy can be directly measured, while…