![](/images/graphics-bg.png)
The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets
Joint Authors
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-09-28
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
In this paper, we study some chaotic properties of s-dimensional dynamical system of the form Ψa1,a2,…,as=gsas,g1a1,…,gs−1as−1, where ak∈Hk for any k∈1,2,…,s, s≥2 is an integer, and Hk is a compact subinterval of the real line ℝ=−∞,+∞ for any k∈1,2,…,s.
Particularly, a necessary and sufficient condition for a cyclic permutation map Ψa1,a2,…,as=gsas,g1a1,…,gs−1as−1 to be LY-chaotic or h-chaotic or RT-chaotic or D-chaotic is obtained.
Moreover, the LY-chaoticity, h-chaoticity, RT-chaoticity, and D-chaoticity of such a cyclic permutation map is explored.
Also, we proved that the topological entropy hΨ of such a cyclic permutation map is the same as the topological entropy of each of the following maps: gj∘gj−1∘⋯∘g1l∘gs∘gs−1∘⋯∘gj+1, if j=1,…,s−1and gs∘gs−1∘⋯∘g1, and that Ψ is sensitive if and only if at least one of the coordinates maps of Ψs is sensitive.
American Psychological Association (APA)
Li, Risong& Lu, Tianxiu. 2020. The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets. Complexity،Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1145549
Modern Language Association (MLA)
Li, Risong& Lu, Tianxiu. The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets. Complexity No. 2020 (2020), pp.1-12.
https://search.emarefa.net/detail/BIM-1145549
American Medical Association (AMA)
Li, Risong& Lu, Tianxiu. The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets. Complexity. 2020. Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1145549
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1145549