Dense periodicity property and Devaney chaos on shifts spaces

2016 ◽  
Vol 10 ◽  
pp. 1019-1029 ◽  
Author(s):  
Malouh Baloush ◽  
Syahida Che Dzul-Kifli ◽  
Chris Good
Keyword(s):  
Devaney Chaos ◽  
Periodicity Property

scholarly journals Some Chaos Notions on Dendrites

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1309
Author(s):  
Asmaa Fadel ◽  
Syahida Che Dzul-Kifli
Keyword(s):  
Dynamical System ◽  
Chaotic Dynamical System ◽  
Devaney Chaos

Transitivity is a key element in a chaotic dynamical system. In this paper, we present some relations between transitivity, stronger and alternative notions of it on compact and dendrite spaces. The relation between Auslander and Yorke chaos and Devaney chaos on dendrites is also discussed. Moreover, we prove that Devaney chaos implies strong dense periodicity on dendrites while the converse is not true.

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 IN A CLASS OF NONCONSTANT WEIGHTED SHIFT OPERATORS

2013 ◽  
Vol 23 (01) ◽  
pp. 1350010 ◽  
Author(s):  
XINXING WU ◽  
PEIYONG ZHU
Keyword(s):  
Positive Integer ◽  
Linear Space ◽  
Normed Linear Space ◽  
Shift Operator ◽  
Weighted Shift ◽  
Constructive Proof ◽  
Sufficient Condition ◽  
Weighted Shift Operator ◽  
Shift Operators ◽  
Devaney Chaos

In this paper, chaos generated by a class of nonconstant weighted shift operators is studied. First, we prove that for the weighted shift operator Bμ : Σ(X) → Σ(X) defined by Bμ(x0, x1, …) = (μ(0)x1, μ(1)x2, …), where X is a normed linear space (not necessarily complete), weak mix, transitivity (hypercyclity) and Devaney chaos are all equivalent to separability of X and this property is preserved under iterations. Then we get that [Formula: see text] is distributionally chaotic and Li–Yorke sensitive for each positive integer N. Meanwhile, a sufficient condition ensuring that a point is k-scrambled for all integers k > 0 is obtained. By using these results, a simple example is given to show that Corollary 3.3 in [Fu & You, 2009] does not hold. Besides, it is proved that the constructive proof of Theorem 4.3 in [Fu & You, 2009] is not correct.

scholarly journals Devaney chaos revisited

2013 ◽  
Vol 160 (3) ◽  
pp. 455-460 ◽  
Author(s):  
Xiaoyi Wang ◽  
Yu Huang
Keyword(s):  
Devaney Chaos

scholarly journals The Retentivity of Chaos under Topological Conjugation

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Tianxiu Lu ◽  
Peiyong Zhu ◽  
Xinxing Wu
Keyword(s):  
Metric Space ◽  
Topological Spaces ◽  
Weak Mixing ◽  
Devaney Chaos ◽  
Topological Conjugation

The definitions of Devaney chaos (DevC), exact Devaney chaos (EDevC), mixing Devaney chaos (MDevC), and weak mixing Devaney chaos (WMDevC) are extended to topological spaces. This paper proves that these chaotic properties are all preserved under topological conjugation. Besides, an example is given to show that the Li-Yorke chaos is not preserved under topological conjugation if the domain is extended to a general metric space.

Devaney chaos and stronger forms of sensitivity on the product of semiflows

2019 ◽  
Vol 98 (3) ◽  
pp. 631-644 ◽  
Author(s):  
Rahul Thakur ◽  
Ruchi Das
Keyword(s):  
Devaney Chaos
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