Strong transitivity properties for operators

被引：22

作者：

Bes, J. ^{[1
]}

Menet, Q. ^{[2
]}

Peris, A. ^{[3
]}

Puig, Y. ^{[4
]}

机构：

[1] Bowling Green State Univ, Dept Math & Stat, Bowling Green, OH 43403 USA

[2] Univ Artois, EA 2462, LML, F-62300 Lens, France

[3] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Edif 8E,4a Planta, E-46022 Valencia, Spain

[4] Univ Calif Riverside, Dept Math, 900 Univ Ave, Riverside, CA 92521 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年 / 266卷 / 2-3期

关键词：

Hypercyclic operators; Furstenberg families; Transitivity properties; Mixing properties; MIXING OPERATORS;

D O I：

10.1016/j.jde.2018.07.076

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a Furstenberg family F of subsets of N, an operator T on a topological vector space X is called F-transitive provided for each non-empty open subsets U, V of X the set {n is an element of Z(+) : T-n (U) boolean AND V not equal empty set} belongs to We classify the topologically transitive operators with a hierarchy of F-transitive subclasses by considering families F that are determined by various notions of largeness and density in Z(+). (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：1313 / 1337

页数：25

共 21 条

[1] Unimodular eigenvalues, uniformly distributed sequences and linear dynamics [J].

Badea, Catalin ;

Grivaux, Sophie .

ADVANCES IN MATHEMATICS, 2007, 211 (02) :766-793

[2]

Bayart F., 2009, CAMB TRACT MATH, V179

[3] Invariant Gaussian measures for operators on Banach spaces and linear dynamics [J].

Bayart, Frederic ;

Grivaux, Sophie .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2007, 94 :181-210

[4] Frequently hypercyclic operators [J].

Bayart, Frederic ;

Grivaux, Sophie .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2006, 358 (11) :5083-5117

[5] Difference sets and frequently hypercyclic weighted shifts [J].

Bayart, Frederic ;

Ruzsa, Imre Z. .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2015, 35 :691-709

[6]

Bergelson V., 2008, Colloq. Math, V110, P117

[7] Recurrence properties of hypercyclic operators [J].

Bes, J. ;

Menet, Q. ;

Peris, A. ;

Puig, Y. .

MATHEMATISCHE ANNALEN, 2016, 366 (1-2) :545-572

[8] Hereditarily hypercyclic operators [J].

Bès, J ;

Peris, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 1999, 167 (01) :94-112

[9]

Bonilla A., 2016, ARXIV160107276V1

[10]

Furstenberg H., 1981, M.B. Porter lectures.

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