Kato Chaos in Linear Dynamics

Lixin Jiao, Lidong Wang () and Heyong Wang
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Lixin Jiao: School of Disciplinary Basics and Applied Statistics, Zhuhai College of Science and Technology (Zhuhai College of Jilin University), Zhuhai 519041, China
Lidong Wang: School of Disciplinary Basics and Applied Statistics, Zhuhai College of Science and Technology (Zhuhai College of Jilin University), Zhuhai 519041, China
Heyong Wang: Department of E-Business, South China University of Technology, Guangzhou 510006, China

Mathematics, 2023, vol. 11, issue 16, 1-9

Abstract: This paper introduces the concept of Kato chaos to linear dynamics and its induced dynamics. This paper investigates some properties of Kato chaos for a continuous linear operator T and its induced operators T ¯ . The main conclusions are as follows: (1) If a linear operator is accessible, then the collection of vectors whose orbit has a subsequence converging to zero is a residual set. (2) For a continuous linear operator defined on Fréchet space, Kato chaos is equivalent to dense Li–Yorke chaos. (3) Kato chaos is preserved under the iteration of linear operators. (4) A sufficient condition is obtained under which the Kato chaos for linear operator T and its induced operators T ¯ are equivalent. (5) A continuous linear operator is sensitive if and only if its inducing operator T ¯ is sensitive. It should be noted that this equivalence does not hold for nonlinear dynamics.

Keywords: Kato chaos; Li–Yorke chaos; Fréchet space; sensitivity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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