scholarly journals Dendrites and Chaos

2018 ◽  
Vol 28 (13) ◽  
pp. 1850158 ◽  
Author(s):  
Tomasz Drwięga
Keyword(s):  
Distributional Chaos ◽  
Dendrite Map

We answer the two questions left open in [Kočan, 2012] i.e. whether there is a relation between [Formula: see text]-chaos and distributional chaos and whether there is a relation between an infinite LY-scrambled set and distributional chaos for dendrite maps. We construct a continuous self-map of a dendrite without any DC3 pairs but containing an uncountable [Formula: see text]-scrambled set. To answer the second question we construct a dendrite [Formula: see text] and a continuous dendrite map without an infinite LY-scrambled set but with DC1 pairs.

The three versions of distributional chaos

2005 ◽  
Vol 23 (5) ◽  
pp. 1581-1583 ◽  
Author(s):  
F. Balibrea ◽  
J. Smı́tal ◽  
M. Štefánková
Keyword(s):  
Distributional Chaos

scholarly journals Distributional chaos for flows

2013 ◽  
Vol 63 (2) ◽  
pp. 475-480
Author(s):  
Yunhua Zhou
Keyword(s):  
Distributional Chaos

A Class of Hyperspace Systems and Distributional Chaos

2014 ◽  
Vol 670-671 ◽  
pp. 1570-1572
Author(s):  
Wei Wang ◽  
Xiao Gang Zhu
Keyword(s):  
Dynamical System ◽  
Difference Equation ◽  
Agricultural Production ◽  
Irrigation District ◽  
Corn Yield ◽  
Primitive Substitution ◽  
Yield Analysis ◽  
Distributional Chaos ◽  
Dynamical Properties ◽  
Ecological Difference

Research on dynamical system has penetrated into many problems of agricultural production, such as prediction of corn yield, analysis on operational situation of irrigation district and research on ecological difference equation. In this paper, we investigated dynamical properties for non-primitive substitution and the set-valued maps induced by the substitution. We proved In two cases that the hyperspace systems induced by non-primitive substitution are not distributional chaotic.

Distributional Chaos on Uniform Spaces

2020 ◽  
Vol 19 (1) ◽  
Author(s):  
Sejal Shah ◽  
Tarun Das ◽  
Ruchi Das
Keyword(s):  
Uniform Spaces ◽  
Distributional Chaos

On the local aspects of distributional chaos

2019 ◽  
Vol 29 (1) ◽  
pp. 013104 ◽  
Author(s):  
Ryszard J. Pawlak ◽  
Anna Loranty
Keyword(s):  
Distributional Chaos

Distributional chaos occurring on measure center

2015 ◽  
Vol 71 ◽  
pp. 55-59 ◽  
Author(s):  
Lidong Wang ◽  
Yan Li ◽  
Jianhua Liang
Keyword(s):  
Distributional Chaos

scholarly journals Devaney Chaos and Distributional Chaos in the Solution of Certain Partial Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Xavier Barrachina ◽  
J. Alberto Conejero
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Semigroups Of Operators ◽  
Partial Differential ◽  
Linear Dynamics ◽  
Distributional Chaos ◽  
Devaney Chaos

The notion of distributional chaos has been recently added to the study of the linear dynamics of operators andC0-semigroups of operators. We will study this notion of chaos for some examples ofC0-semigroups that are already known to be Devaney chaotic.

CHAOS ON ONE-DIMENSIONAL COMPACT METRIC SPACES

2012 ◽  
Vol 22 (10) ◽  
pp. 1250259 ◽  
Author(s):  
ZDENĚK KOČAN
Keyword(s):  
Topological Entropy ◽  
Metric Spaces ◽  
Chaotic Behavior ◽  
Homoclinic Trajectory ◽  
One Dimensional ◽  
Distributional Chaos ◽  
Compact Metric Spaces ◽  
Continuous Maps

We consider various kinds of chaotic behavior of continuous maps on compact metric spaces: the positivity of topological entropy, the existence of a horseshoe, the existence of a homoclinic trajectory (or perhaps, an eventually periodic homoclinic trajectory), three levels of Li–Yorke chaos, three levels of ω-chaos and distributional chaos of type 1. The relations between these properties are known when the space is an interval. We survey the known results in the case of trees, graphs and dendrites.

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