Sets of periods for chaotic linear operators

Conejero, J. Alberto; Martínez-Giménez, Félix; Peris, Alfredo; Ródenas, F.

doi:10.1007/s13398-020-00996-z

Cited by 4 publications

(1 citation statement)

References 23 publications

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“…A uniform treatment of Li-Yorke chaos, mean Li-Yorke chaos and distributional chaos for continuous endomorphisms of completely metrizable groups is given by Jiang [19]. For more recent work in linear dynamics, refer to [20][21][22][23]. The above works show that chaos in linear dynamical systems can also produce very complex behaviors.…”

Section: Introductionmentioning

confidence: 99%

Kato Chaos in Linear Dynamics

Jiao

Wang

2023

Mathematics

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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.

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