Invariance of chaos from backward shift on the Köthe sequence space

Xinxing Wu; Guanrong Chen; Peiyong Zhu

doi:10.1088/0951-7715/27/2/271

Invariance of chaos from backward shift on the Köthe sequence space

Xinxing Wu^*, Guanrong Chen, Peiyong Zhu

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

22 Citations (Scopus)

Abstract

In this paper it is proved that the backward shift operator on the Köthe sequence space admits a pair which is not asymptotic, if and only if it has an uncountable invariant ε-scrambled set for some ε > 0, if and only if it has an ε-scrambled subspace for some ε > 0, if and only if it has an invariant scrambled linear manifold. An analogous result for distributional chaos of type 2 is also obtained. © 2014 IOP Publishing Ltd & London Mathematical Society

Original language	English
Pages (from-to)	271-288
Journal	Nonlinearity
Volume	27
Issue number	2
Online published	17 Jan 2014
DOIs	https://doi.org/10.1088/0951-7715/27/2/271
Publication status	Published - Jan 2014

Research Keywords

backward shift
distributional chaos
invariant set (linear manifold)
Li-Yorke chaos

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abstract = "In this paper it is proved that the backward shift operator on the K{\"o}the sequence space admits a pair which is not asymptotic, if and only if it has an uncountable invariant ε-scrambled set for some ε > 0, if and only if it has an ε-scrambled subspace for some ε > 0, if and only if it has an invariant scrambled linear manifold. An analogous result for distributional chaos of type 2 is also obtained. {\textcopyright} 2014 IOP Publishing Ltd & London Mathematical Society",

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author = "Xinxing Wu and Guanrong Chen and Peiyong Zhu",

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T1 - Invariance of chaos from backward shift on the Köthe sequence space

AU - Wu, Xinxing

AU - Chen, Guanrong

AU - Zhu, Peiyong

PY - 2014/1

Y1 - 2014/1

N2 - In this paper it is proved that the backward shift operator on the Köthe sequence space admits a pair which is not asymptotic, if and only if it has an uncountable invariant ε-scrambled set for some ε > 0, if and only if it has an ε-scrambled subspace for some ε > 0, if and only if it has an invariant scrambled linear manifold. An analogous result for distributional chaos of type 2 is also obtained. © 2014 IOP Publishing Ltd & London Mathematical Society

AB - In this paper it is proved that the backward shift operator on the Köthe sequence space admits a pair which is not asymptotic, if and only if it has an uncountable invariant ε-scrambled set for some ε > 0, if and only if it has an ε-scrambled subspace for some ε > 0, if and only if it has an invariant scrambled linear manifold. An analogous result for distributional chaos of type 2 is also obtained. © 2014 IOP Publishing Ltd & London Mathematical Society

KW - backward shift

KW - distributional chaos

KW - invariant set (linear manifold)

KW - Li-Yorke chaos

UR - http://www.scopus.com/inward/record.url?scp=84894274197&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84894274197&origin=recordpage

U2 - 10.1088/0951-7715/27/2/271

DO - 10.1088/0951-7715/27/2/271

M3 - RGC 21 - Publication in refereed journal

SN - 0951-7715

VL - 27

SP - 271

EP - 288

JO - Nonlinearity

JF - Nonlinearity

IS - 2

ER -

Invariance of chaos from backward shift on the Köthe sequence space

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