Distributional chaos for linear operators

被引：69
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
收藏
页码：2143 / 2163
页数：21
相关论文
共 24 条
  • [1] [Anonymous], DYNAMICS LINEAR OPER
  • [2] Hypercyclicity and unimodular point spectrum
    Bayart, F
    Grivaux, S
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 226 (02) : 281 - 300
  • [3] Bayart F., ARXIV13052325
  • [4] Invariant Gaussian measures for operators on Banach spaces and linear dynamics
    Bayart, Frederic
    Grivaux, Sophie
    [J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2007, 94 : 181 - 210
  • [5] Frequently hypercyclic operators
    Bayart, Frederic
    Grivaux, Sophie
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (11) : 5083 - 5117
  • [6] Beauzamy B., 1988, North-Holland Math Library
  • [7] Li-Yorke and distributionally chaotic operators
    Bermudez, T.
    Bonilla, A.
    Martinez-Gimenez, F.
    Peris, A.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 373 (01) : 83 - 93
  • [8] Bernardes Jr N. C., 2012, PREPRINT
  • [9] Frequently hypercyclic operators and vectors
    Bonilla, A.
    Grosse-Erdmann, K. -G.
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2007, 27 : 383 - 404
  • [10] El-Fallah O, 2004, J OPERAT THEOR, V52, P89
123