Distributional chaos for linear operators

被引：70

作者：

Bernardes, N. C., Jr. ^{[1
]}

Bonilla, A. ^{[2
]}

Mueller, V.

Peris, A. ^{[3
,4
]}

机构：

[1] Univ Fed Rio de Janeiro, Inst Matemat, Dept Matemat Aplicada, BR-21945970 Rio De Janeiro, RJ, Brazil

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

[3] Acad Sci Czech Republ, Math Inst, CR-11567 Prague 1, Czech Republic

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

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 265卷 / 09期

关键词：

Distributional chaos; Hypercyclic operators; Irregular vectors; INVARIANT;

D O I：

10.1016/j.jfa.2013.06.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize distributional chaos for linear operators on Frechet spaces in terms of a computable condition (DCC), and also as the existence of distributionally it-regular vectors. A sufficient condition for the existence of dense uniformly distributionally irregular manifolds is presented, which is very general and can be applied to many classes of operators. Distributional chaos is also analyzed in connection with frequent hypercyclicity, and the particular cases of weighted shifts and composition operators are given as an illustration of the previous results. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：2143 / 2163

页数：21

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