Related papers: Li-Yorke and distributionally chaotic operators
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 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…
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,…
We prove that if X is any complex separable infinite-dimensional Banach space with an unconditional Schauder decomposition, X supports an operator T which is chaotic and frequently hypercyclic. In contrast with the complex case, we observe…
In this paper, we discuss the relationship between Li-Yorke chaos and distributional chaos in a sequence. We point out the set of all distributional $\delta$-scramble pairs in the sequence $Q$ is a $G_\delta$ set, and prove that Li-Yorke…
It is rigorously proved that the chaotic dynamics of the non-smooth system with relay function is persistent even if a chaotic perturbation is applied. We consider chaos in a modified Li-Yorke sense such that infinitely many almost periodic…
In this paper, we study distributional chaos for weighted translations on locally compact groups. We give a sufficient condition for such operators to be distributionally chaotic and construct an example of distributionally chaotic weighted…
By strengthening one of the hypotheses of a well-known sufficient condition for the hypercyclicity of linear operators in Banach spaces, we arrive at a sufficient condition for linear chaos and reveal consequences of the latter for…
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…
We answer one of the main current questions in Linear Dynamics by constructing a chaotic operator on $\ell^1$ which is not $\mathcal{U}$-frequently hypercyclic and thus not frequently hypercyclic. This operator also gives us an example of a…
We introduce the definition of Li-Yorke chaos for the map f on G-spaces, and show G-Li-Yorke chaos is iterable for f. Li-Yorke chaos implies G-Li-Yorke chaos, while the converse is not true. Then we give a sufficient condition for f to be…
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.…
We explore distributional chaos for $C_0$-semigroups of linear operators on Banach spaces whose index set is a sector in the complex plane. We establish the relationship between distributional sensitivity and distributional chaos by…
If an invertible linear dynamical systems is Li-York chaotic or other chaotic, what's about it's inverse dynamics? what's about it's adjoint dynamics? With this unresolved but basic problems, this paper will give a criterion for Lebesgue…
In our another recent article, we introduce a new dynamical property for linear operators called norm-unimodality which implies distributional chaos. In the present paper, we'll give a further discussion of norm-unimodality. It is showed…
Recently, in connection with C*-algebra theory, the first author and Danilo Royer introduced ultragraph shift spaces. In this paper we define a family of metrics for the topology in such spaces, and use these metrics to study the existence…
We study density properties of orbits for a hypercyclic operator $T$ on a separable Banach space $X$, and show that exactly one of the following four cases holds: (1) every vector in $X$ is asymptotic to zero with density one; (2) generic…
We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. To achieve this, we study $\mathcal F$-hypercyclicity for a family of subsets of the…
Chaotic linear dynamics deals primarily with various topological ergodic properties of semigroups of continuous linear operators acting on a topological vector space. We treat questions of characterizing which of the spaces from a given…
In this article, we show that a chaotic behavior can be found on a cube with arbitrary finite dimension. That is, the cube is a quasi-minimal set with Poincare chaos. Moreover, the dynamics is shown to be Devaney and Li-Yorke chaotic. It…