Measurable Sensitivity for Semi-Flows

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 nu...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-12, Vol.11 (23), p.4763
Main Authors: Quan, Weizhen, Lu, Tianxiu, Li, Risong, Chen, Yuanlin, Ding, Xianfeng, Li, Yongjiang
Format: Article
Language:English
Subjects:
Analysis
Conformal mapping
Eigenvalues
Initial conditions
Isomorphism
measurable sensitivity
measure-preserving transformation
Methods
semi-flows
Sensitivity
Sensitivity analysis
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11234763