# Li–Yorke and distributionally chaotic operators

@article{Bermdez2010LiYorkeAD, title={Li–Yorke and distributionally chaotic operators}, author={Teresa Berm{\'u}dez and A. Bonilla and F. Mart'inez-Gim'enez and Alfredo Peris}, journal={Journal of Mathematical Analysis and Applications}, year={2010}, volume={373}, pages={83-93} }

## 84 Citations

### DISTRIBUTIONAL CHAOS AND LI — YORKE CHAOS IN METRIC SPACES

- Mathematics
- 2019

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…

### Li–Yorke chaos in linear dynamics

- MathematicsErgodic Theory and Dynamical Systems
- 2014

We obtain new characterizations of Li–Yorke chaos for linear operators on Banach and Fréchet spaces. We also offer conditions under which an operator admits a dense set or linear manifold of…

### Li–Yorke chaos for composition operators on $$L^p$$Lp-spaces

- MathematicsMonatshefte für Mathematik
- 2019

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…

### Li-Yorke Chaotic Properties of Abstract Di ff erential Equations of First Order

- Mathematics
- 2016

In this paper, we analyze the Li-Yorke chaotic properties of abstract non-degenerate differential equations of first order in Banach and Fréchet spaces. We investigate the property of Li-Yorke chaos…

### Reiterative Distributional Chaos on Banach Spaces

- MathematicsInt. J. Bifurc. Chaos
- 2019

The notions of reiterative distributional chaos of types $1$, $1^+$ and $2$ for continuous linear operators on Banach spaces, which are characterized in terms of the existence of an irregular vector with additional properties, are introduced.

### Li-Yorke chaos for composition operators on Orlicz spaces

- Mathematics
- 2022

. In this paper we characterize Li-Yorke chaotic composition operators on Orlicz spaces. Indeed some necessary and suﬃcient conditions are provided for Li-Yorke chaotic composition operator C ϕ on…

### Investigating Distributional Chaos for Operators on Fréchet Spaces

- MathematicsInt. J. Bifurc. Chaos
- 2021

In this paper, various notions of chaos for continuous linear operators on Fréchet spaces are investigated. It is shown that an operator is Li–Yorke chaotic if and only if it is mean Li–Yorke chaotic…

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