Related papers: Dynamical metric order
It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, due to quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal…
The standard definition of the dimension of a vector space or rank of a module states that dimension or rank is equal to the cardinality of any basis, which requires an understanding of the concepts of basis, generating set, and linear…
We introduce a fractal dimension for a metric space defined in terms of the persistent homology of extremal subsets of that space. We exhibit hypotheses under which this dimension is comparable to the upper box dimension; in particular, the…
In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time,…
We consider positively supported Borel measures for which all moments exist. On the set of compactly supported measures in this class a partial order is defined via eventual dominance of the moment sequences. Special classes are identified…
We give sufficient conditions for a finite metric space to be determined by the magnitude function. In particular, a generic finite metric space such that the distances between the points are rationally independent is determined by the…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
In this paper, we extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We introduce the notion of a partial isometry in an absolute…
Let $(X,d,f)$ be a topological dynamical system, where $(X,d)$ is a compact metric space and $f:X\to X$ is a continuous map. We define $n$-ordered empirical measure of $x\in X$ by \begin{align*}…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
The concept of a quasi-metric space arises by relaxing the requirement of the symmetry axiom in the definition of a metric. This small variation alters several structural properties possessed by a standard metric space. This article aims to…
The purpose of this paper is twofold. Firstly, the new matrix domains are constructed with the new infinite matrices and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix…
In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…
This paper studies distributional chaos in non-autonomous discrete systems generated by given sequences of maps in metric spaces. In the case that the metric space is compact, it is shown that a system is Li-Yorke{\delta}-chaotic if and…
In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be…
In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in $\mathbb{D}$. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some…
Let $f: M\rightarrow M$ be a continuous map on a compact metric space $M$ equipped with a fixed metric $d$, and let $\tau$ be the topology on $M$ induced by $d$. First, we will establish some fundamental properties of the mean Hausdorff…
The aim of this paper is to prove the existence of inductive and inverse limits of direct and inverse systems in a certain category of compact metric spaces as well as of compact metric groups. Some applications are presented.
Successive divisions of compact metric spaces appear in many different areas of mathematics such as the construction of self-similar sets, Markov partitions associated with hyperbolic dynamical systems, dyadic cubes associated with a…
These notes follow my articles [1, 6], and give some new important details. We propose here a new combinatorial method of encoding of measure spaces with measure preserving transformations, (or groups of transformations) in order to give…