Measurable Sensitivity for Semi-Flows

Weizhen Quan, Tianxiu Lu (), Risong Li (), Yuanlin Chen, Xianfeng Ding and Yongjiang Li
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Weizhen Quan: Department of Mathematics, Zhanjiang Preschool Education College, Zhanjiang 524037, China
Tianxiu Lu: College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
Risong Li: School of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524025, China
Yuanlin Chen: 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 23, 1-9

Abstract: Sensitive dependence on initial conditions is a crucial characteristic of chaos. The concept of measurable sensitivity (MS) was introduced as a measure-theoretic version of sensitive dependence on initial conditions. Their research demonstrated that MS arises from light mixing, indicates a finite number of eigenvalues for a transformation, and is not present in the case of infinite measure preservation. Unlike the traditional understanding of sensitivity, MS carries up to account for isomorphism in the sense of measure theory, which ignores the function’s behavior on null sets and eliminates dependence on the chosen metric. Inspired by the results of James on MS, this paper generalizes some of the concepts (including MS) that they used in their study of MS for conformal transformations to semi-flows, and generalizes their main results in this regard to semi-flows.

Keywords: semi-flows; measure-preserving transformation; measurable sensitivity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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