devaney chaos
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Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1309
Author(s):  
Asmaa Fadel ◽  
Syahida Che Dzul-Kifli

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.



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




2017 ◽  
Vol 15 (1) ◽  
pp. 948-958 ◽  
Author(s):  
Chung-Chuan Chen ◽  
J. Alberto Conejero ◽  
Marko Kostić ◽  
Marina Murillo-Arcila

Abstract We introduce several notions of linear dynamics for multivalued linear operators (MLO’s) between separable Fréchet spaces, such as hypercyclicity, topological transitivity, topologically mixing property, and Devaney chaos. We also consider the case of disjointness, in which any of these properties are simultaneously satisfied by several operators. We revisit some sufficient well-known computable criteria for determining those properties. The analysis of the dynamics of extensions of linear operators to MLO’s is also considered.



2017 ◽  
Vol 13 (01) ◽  
pp. 19-21
Author(s):  
Vincent. N. S ◽  
Vinod Kumar
Keyword(s):  


2016 ◽  
Vol 26 (11) ◽  
pp. 1650190 ◽  
Author(s):  
Hao Zhu ◽  
Yuming Shi ◽  
Hua Shao

This paper is concerned with Devaney chaos in nonautonomous discrete systems. It is shown that in its definition, the two former conditions, i.e. transitivity and density of periodic points, in a set imply the last one, i.e. sensitivity, in the case that the set is unbounded, while a similar result holds under two additional conditions in the other case that the set is bounded. Some chaotic behavior is studied for a class of nonautonomous discrete systems, each of which is governed by a convergent sequence of continuous maps. In addition, the concepts of some pseudo-orbits and shadowing properties are introduced for nonautonomous discrete systems, and it is shown that some shadowing properties of the system and density of periodic points imply that the system is Devaney chaotic under the condition that the sequence of continuous maps is uniformly convergent in a compact metric space.



2016 ◽  
Vol 26 (9) ◽  
pp. 093103 ◽  
Author(s):  
Jian Li ◽  
Jie Li ◽  
Siming Tu


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


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