Li-Yorke and distributionally chaotic operators

被引：81

作者：

Bermudez, T. ^{[2
]}

Bonilla, A. ^{[2
]}

Martinez-Gimenez, F. ^{[1
]}

Peris, A. ^{[1
]}

机构：

[1] Univ Politecn Valencia, Dept Matemat Aplicada, IUMPA, Valencia 46022, Spain

[2] Univ La Laguna, Dept Anal Matemat, San Cristobal la Laguna 38271, Tenerife, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 373卷 / 01期

关键词：

Li-Yorke chaos; Distributional chaos; Irregular vector; Distributionally irregular vectors; Weighted shift operators; HYPERCYCLIC OPERATORS; DYNAMICAL-SYSTEMS; EXISTENCE; SEMIGROUPS; SPACE;

D O I：

10.1016/j.jmaa.2010.06.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study Li-Yorke chaos and distributional chaos for operators on Banach spaces. More precisely, we characterize Li-Yorke chaos in terms of the existence of irregular vectors. Sufficient "computable" criteria for distributional and Li-Yorke chaos are given, together with the existence of dense scrambled sets under some additional conditions. We also obtain certain spectral properties. Finally, we show that every infinite dimensional separable Banach space admits a distributionally chaotic operator which is also hypercyclic. (c) 2010 Elsevier Inc. All rights reserved.

引用

页码：83 / 93

页数：11

共 31 条

[1] Existence of hypercyclic operators on topological vector spaces [J].

Ansari, SI .

JOURNAL OF FUNCTIONAL ANALYSIS, 1997, 148 (02) :384-390

[2]

Bayart F, 2009, DYNAMICS LINEAR OPER

[3]

Beauzamy B., 1988, North-Holland Math Library

[4] Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces [J].

Bermúdez, T ;

Bonilla, A ;

Conejero, JA ;

Peris, A .

STUDIA MATHEMATICA, 2005, 170 (01) :57-75

[5] On the existence of chaotic and hypercyclic semigroups on banach spaces [J].

Bermúdez, T ;

Bonilla, A ;

Martinón, A .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 131 (08) :2435-2441

[6] On hypercyclic operators on Banach spaces [J].

Bernal-González, L .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (04) :1003-1010

[7] Existence and nonexistence of hypercyclic semigroups [J].

Bernal-Gonzalez, L. ;

Grosse-Erdmann, K. -G. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (03) :755-766

[8] A Banach space which admits no chaotic operator [J].

Bonet, J ;

Martínez-Giménez, F ;

Peris, A .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2001, 33 :196-198

[9] Hypercyclic operators on non-normable Frechet spaces [J].

Bonet, J ;

Peris, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 159 (02) :587-595

[10] COMPLEX GEOMETRY AND OPERATOR THEORY [J].

COWEN, MJ ;

DOUGLAS, RG .

ACTA MATHEMATICA, 1978, 141 (3-4) :187-261

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