相关论文: Chaos for Cowen-Douglas operators
Chaotic iterations, a tool formerly used in distributed computing, has recently revealed various interesting properties of disorder leading to its use in the computer science security field. In this paper, a comprehensive study of its…
We show that the existence of a dense set of periodic points for a topologically transitive non-minimal continuous group action on a Hausdorff uniform space with an infinite acting group does not necessarily imply a sensitive dependence to…
We explore connections among the regional proximal relation, the asymptotic relation and the distal relation for a topological dynamical system with the shadowing property, and show that if a Devaney chaotic system has the shadowing…
This paper is concerned with Devaney chaos in non-autonomous discrete systems. It is shown that in its definition, the two former conditions, i.e., transitivity and density of periodic points, in a set imply the last one, i.e., sensitivity,…
In this paper, we study various chaos of topological group or semigroup actions.
In this paper, we study the Li-Yorke chaotic composition operators on Orlicz-Lorentz space. In fact, necessary and sufficient conditions are given for Li-Yorke chaotic composition operator $C_{\tau}$ on $\mathbb{L}^{\varphi,h}(\mu)$.…
We show that linear chaos in the space $c(\mathbb{N})$ of convergent sequences cannot be arrived at by merely extending the weighted backward shifts in the space $c_0(\mathbb{N})$ of vanishing sequences. Applying a newly found sufficient…
We analyze from the viewpoint of an abstract Markov operator recent results by Nualart and Peccati, and Nourdin and Peccati, on the fourth moment as a condition on a Wiener chaos to have a distribution close to Gaussian. In particular, we…
In this paper, we characterize Li-Yorke chaotic generalized weighted shift operators on the standard Hilbert module over the C*-algebra of compact operators on a separable Hilbert space in terms of operator-valued weights of these shifts.…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
Design and cryptanalysis of chaotic encryption schemes are major concerns to provide secured information systems. Pursuing our previous research works, some well-defined discrete chaotic iterations that satisfy the reputed Devaney's…
We present a definition of chaotic Delone set, and establish the genericity of chaos in the space of $(\epsilon,\delta)$-Delone sets for $\epsilon\geq \delta$. We also present a hyperbolic analogue of the cut-and-project method that…
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a novel theorem demonstrating how nonlinear dynamics within a…
In this paper we consider the question of distributional chaos on non-compact metric dynamical systems. We focus on a shift space over a countable alphabet, the Baire Space. We prove that on the Baire Space subshifts of finite type exhibit…
This chapter provides an overview of chaotic billiard lasers as a prominent branch of quantum chaos. These lasers offer an ideal experimental platform for demonstrating the principles of quantum chaos within a physical system. We begin by…
In this paper, we study certain Banach spaces of analytic functions on which a left-invertible multiplication operator acts. It turns out that, under natural conditions, its left inverse is a Cowen-Douglas operator. We investigate how the…
A sufficient and necessary condition ensuring that the backward shift operator on the K\"{o}the sequence space admits an invariant distributionally $\varepsilon$-scrambled set for some $\varepsilon>0$ is obtained, improving the main results…
We study Li--Yorke and mean Li--Yorke chaos for weighted composition operators $C_{w,\varphi}$ on Banach spaces of analytic functions on the unit disk $\mathbb{D}$. Under natural conditions on the space, we show that $C_{w,\varphi}$ is…
We utilize the idea underlying the construct of the classical weighted backward shift Rolewicz's operators to furnish a straightforward approach to a general construct of chaotic unbounded linear operators in a (real or complex) Banach…
We discuss Devaney chaos on compact metric spaces using a decomposition space characterized by topological nature of symbolic dynamics. A chaotic map obtained here is defined as a topologically conjugate of the chaotic map on a…