The Ergodicity and Sensitivity of Nonautonomous Discrete Dynamical Systems

Risong Li, Tianxiu Lu (), Hongqing Wang (), Jie Zhou, Xianfeng Ding and Yongjiang Li
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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
Hongqing Wang: School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China
Jie Zhou: College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
Xianfeng Ding: School of Science, Southwest Petroleum University, Chengdu 610500, China
Yongjiang Li: School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China

Mathematics, 2023, vol. 11, issue 6, 1-15

Abstract: Let ( E , h 1 , ∞ ) be a nonautonomous discrete dynamical system (briefly, N.D.D.S.) that is defined by a sequence ( h j ) j = 1 ∞ of continuous maps h j : E → E over a nontrivial metric space ( E , d ) . This paper defines and discusses some forms of ergodicity and sensitivity for the system ( E , h 1 , ∞ ) by upper density, lower density, density, and a sequence of positive integers. Under some conditions, if the rate of convergence at which ( h j ) j = 1 ∞ converges to the limit map h is “fast enough” with respect to a sequence of positive integers with a density of one, it is shown that several sensitivity properties for the N.D.D.S. ( E , h 1 , ∞ ) are the same as those properties of the system ( E , h ) . Some sufficient conditions for the N.D.D.S. ( E , h 1 , ∞ ) to have stronger sensitivity properties are also presented. The conditions in our results are less restrictive than those in some existing works, and the conclusions of all the theorems in this paper improve upon those of previous studies. Thus, these results are extensions of the existing ones.

Keywords: nonautonomous discrete dynamical systems; ergodicity; sensitivity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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