Distributional Chaos and Sensitivity for a Class of Cyclic Permutation Maps

Yu Zhao, Waseem Anwar, Risong Li (), Tianxiu Lu () and Zhiwen Mo
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Yu Zhao: School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China
Waseem Anwar: Department of Mathematics, Sichuan Normal University, Chengdu 610017, China
Risong Li: School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China
Tianxiu Lu: College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
Zhiwen Mo: Department of Mathematics, Sichuan Normal University, Chengdu 610017, China

Mathematics, 2023, vol. 11, issue 15, 1-9

Abstract: Several chaotic properties of cyclic permutation maps are considered. Cyclic permutation maps refer to p -dimensional dynamical systems of the form φ ( b 1 , b 2 , ⋯ , b p ) = ( u p ( b p ) , u 1 ( b 1 ) , ⋯ , u p − 1 ( b p − 1 ) ) , where b j ∈ H j ( j ∈ { 1 , 2 , ⋯ , p } ), p ≥ 2 is an integer, and H j ( j ∈ { 1 , 2 , ⋯ , p } ) are compact subintervals of the real line R = ( − ∞ , + ∞ ) . u j : H j → H j + 1 ( j = 1 , 2 , … , p − 1 ) and u p : H p → H 1 are continuous maps. Necessary and sufficient conditions for a class of cyclic permutation maps to have Li–Yorke chaos, distributional chaos in a sequence, distributional chaos, or Li–Yorke sensitivity are given. These results extend the existing ones.

Keywords: cyclic permutation map; sensitivity; chaos (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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