Related papers: $C^{*}$ algebra and inverse chaos
In this paper, we give two examples to show that an invertible mapping is Li-Yorke chaotic does not imply its inverse being Li-Yorke chaotic, in which one is an invertible bounded linear operator on an infinite dimensional Hilbert space and…
We show that a linear quantum harmonic oscillator is chaotic in the sense of Li-Yorke. We also prove that the weighted backward shift map, used as an infinite dimensional linear chaos model, in a separable Hilbert space is chaotic in the…
In this paper, we introduce several new types and generalizations of the concepts distributional chaos and Li-Yorke chaos. We consider the general sequences of binary relations acting between metric spaces, while in a separate section we…
This article is intended to outline some the recent work by the author on the chaoticity of some specific bakward shift unbounded operators realized as differential operators acting on some Fock-Bargmann spaces and give suficient conditions…
Li-Yorke chaos is a popular and well-studied notion of chaos. Several simple and useful characterizations of this notion of chaos in the setting of linear dynamics were obtained recently. In this note we show that even simpler and more…
In this article, we provide a sufficient condition which gives Devaney chaos and distributional chaos for Cowen-Douglas operators. In fact, we obtain a distributionally chaotic criterion for bounded linear operators on Banach spaces.
We study Li-Yorke chaos and distributional chaos for operators on Banach spaces. More precisely, we characterize Li-Yorke chaos in terms of the existence of irregular vectors. Sufficient "computable" criteria for distributional and Li-Yorke…
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…
This paper is concerned with strong Li-Yorke chaos induced by A-coupled-expansion for time-varying (i.e., nonautonomous) discrete systems in metric spaces. Some criteria of chaos in the strong sense of Li-Yorke are established via strict…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
This paper focuses on the dense uniform Li-Yorke chaos for linear operators on a Banach space. Some sufficient conditions and equivalent conditions are established under which the dynamical system is densely uniformly Li-Yorke chaotic. It…
We establish complete characterizations of the notion of Li-Yorke chaos for weighted composition operators on $C_0(X)$ spaces and on $L^p(\mu)$ spaces. As a consequence, we obtain simple characterizations of the Li-Yorke chaotic weighted…
In this paper we characterize Li-Yorke chaotic composition operators on Orlicz spaces. Indeed some necessary and suffcient conditions are provided for Li-Yorke chaotic composition operator C' on the Orlicz space Lp. In some cases we have…
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 $\mathbb{L}^{\varphi,h}(\mu)$.…
In order to study Li-Yorke chaos by the scalar perturbation for a given bounded linear operator $T$ on Banach spaces $X$, we introduce the Li-Yorke chaos translation set of $T$, which is defined by…
We study Li-Yorke chaos for sequences of continuous linear operators from an \(F\)-space to a normed space. We introduce the \emph{D-phenomenon} to establish a common dense lineable criterion that encompasses properties such as recurrence,…
The main aim of this paper is to consider various notions of (dense) disjoint Li-Yorke chaos for general sequences of multivalued linear operators in Fr\' echet spaces. We also consider continuous analogues of introduced notions and provide…
This paper establishes some criteria of chaos in non-autonomous discrete systems. Several criteria of strong Li-Yorke chaos are given. Based on these results, some criteria of distributional chaos in a sequence are established. Moreover,…
For a positive and invertible linear operator $T$ acting on a $C^*$-algebra, we give necessary and sufficient criteria for the inverse operator $T^{-1}$ to be positive, too. Moreover, a simple counterexample shows that $T^{-1}$ need not be…
It is proved that positive entropy implies mean Li-Yorke chaos for a G-system, where G is a countable infinite discrete bi-orderable amenable group. Examples are given for the cases of integer lattice groups and groups of integer unipotent…