Maximal distributional chaos of weighted shift operators on Köthe sequence spaces

被引：0

作者：

Xinxing Wu

机构：

[1] University of Electronic Science and Technology of China,School of Mathematics

来源：

Czechoslovak Mathematical Journal | 2014年 / 64卷

关键词：

weighted shift operator; principal measure; distributional chaos; 37D45; 54H20; 37B40; 26A18; 28D20;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

During the last ten some years, many research works were devoted to the chaotic behavior of the weighted shift operator on the Köthe sequence space. In this note, a sufficient condition ensuring that the weighted shift operator Bwn: λp(A) → λp(A) defined on the Köthe sequence space λp(A) exhibits distributional ɛ-chaos for any 0 < ɛ < diamλp(A) and any n ∈ ℕ is obtained. Under this assumption, the principal measure of Bwn is equal to 1. In particular, every Devaney chaotic shift operator exhibits distributional ɛ-chaos for any 0 < ɛ < diam λp(A).

引用

页码：105 / 114

页数：9

共 29 条

[1]

Bermúdez T.(2011)Li-Yorke and distributionally chaotic operators J. Math. Anal. Appl. 373 83-93

[2]

Bonilla A.(1999)A linear chaotic quantum harmonic oscillator Appl. Math. Lett. 12 15-19

[3]

Martínez-Giménez F.(1975)Period three implies chaos Am. Math. Mon. 82 985-992

[4]

Peris A.(2009)Distributional chaos for backward shifts J. Math. Anal. Appl. 351 607-615

[5]

Duan J.(2007)Chaos for power series of backward shift operators Proc. Am. Math. Soc. 135 1741-1752

[6]

Fu X.-C.(2007)Shift spaces and distributional chaos Chaos Solitons Fractals 31 347-355

[7]

Liu P.-D.(2007)On some notions of chaos in dimension zero Colloq. Math. 107 167-177

[8]

Manning A.(1994)Measures of chaos and a spectral decomposition of dynamical systems on the interval Trans. Am. Math. Soc. 344 737-754

[9]

Li T. Y.(2000)Distributional (and other) chaos and its measurement Real Anal. Exch. 26 495-524

[10]

Yorke J. A.(2004)Distributional chaos for triangular maps Chaos Solitons Fractals 21 1125-1128

← 1 2 3 →