Related papers: Weakly mixing, topologically weakly mixing, and se…

Rational weak mixing is a measure theoretic version of Krickeberg's strong ratio mixing property for infinite measure preserving transformations. It requires "{\tt density}" ratio convergence for every pair of measurable sets in a dense…

Let (X,T) be a dynamical system, where X is a compact metric space and T a continuous onto map. For weak Gibbs measures we prove large deviations estimates.

The question we deal with here, which was presented to us by Joe Auslander and Anima Nagar, is whether there is a nontrivial cascade (X,T) whose enveloping semigroup, as a dynamical system, is topologically weakly mixing (WM). After an…

A note on the property of weak contraction, which implies that all bounded solutions of a nonlinear system converge to a (possibly non-unique) equilibrium. We provide some simple results about interconnections of such systems, and a brief…

In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…

Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs…

Weak amplification is a signal enhancement technique which is used to measure tiny changes that otherwise cannot be determined because of technical limitations. It is based on the existence of a special type of interaction which couples a…

In this paper notions of strong specification property and quasi-weak specification property for non-autonomous discrete systems are introduced and studied. It is shown that these properties are dynamical properties and are preserved under…

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…

Dynamical compactness with respect to a family as a new concept of chaoticity of a dynamical system was introduced and discussed in [22]. In this paper we continue to investigate this notion. In particular, we prove that all dynamical…

Weak values are typically obtained experimentally by performing weak measurements, which involve weak interactions between the measured system and a probe. However, the determination of weak values does not necessarily require weak…

This article investigates weak convergence of the sequential $d$-dimensional empirical process under strong mixing. Weak convergence is established for mixing rates $\alpha_n = O(n^{-a})$, where $a>1$, which slightly improves upon existing…

Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing…

A technique is presented for multiplexing two ergodic measure preserving transformations together to derive a third limiting transformation. This technique is used to settle a question regarding rigidity of weak mixing transformations.…

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially…

The goal of this article is to study how combinatorial equivalence implies topological conjugacy. For that, we introduce the concept of kneading sequences for nonautonomous discrete dynamical systems and show that these sequences are a…

The problem of feedback control of quantum systems by means of weak measurements is investigated in detail. When weak measurements are made on a set of identical quantum systems, the single-system density matrix can be determined to a high…

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 weak measurement on a system is made by coupling a pointer weakly to the system and then measuring the position of the pointer. If the initial wavefunction for the pointer is real, the mean displacement of the pointer is proportional to…

Weakly chaotic or weakly interacting systems have a wide regime where the common random matrix theory modeling does not apply. As an example we consider cold atoms in a nearly integrable optical billiard with displaceable wall ("piston").…