Strong transitivity properties for operators

J. Bès; Q. Menet; A. Peris; Y. Puig

doi:10.1016/j.jde.2018.07.076

Strong transitivity properties for operators

J. Bès
, Q. Menet
, A. Peris
, Y. Puig

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

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∈Z₊:Tⁿ(U)∩V≠∅} belongs to F. 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₊.

Original language	English
Pages (from-to)	1313-1337
Number of pages	25
Journal	Journal of Differential Equations
Volume	266
Issue number	2-3
DOIs	https://doi.org/10.1016/j.jde.2018.07.076
State	Published - 15 Jan 2019
Externally published	Yes

Keywords

Furstenberg families
Hypercyclic operators
Mixing properties
Transitivity properties

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2018.07.076

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title = "Strong transitivity properties for operators",

abstract = "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∈Z+:Tn(U)∩V≠∅\} belongs to F. 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+.",

keywords = "Furstenberg families, Hypercyclic operators, Mixing properties, Transitivity properties",

author = "J. B{\`e}s and Q. Menet and A. Peris and Y. Puig",

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T1 - Strong transitivity properties for operators

AU - Bès, J.

AU - Menet, Q.

AU - Peris, A.

AU - Puig, Y.

PY - 2019/1/15

Y1 - 2019/1/15

N2 - 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∈Z+:Tn(U)∩V≠∅} belongs to F. 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+.

AB - 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∈Z+:Tn(U)∩V≠∅} belongs to F. 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+.

KW - Furstenberg families

KW - Hypercyclic operators

KW - Mixing properties

KW - Transitivity properties

UR - https://www.scopus.com/pages/publications/85050886361

U2 - 10.1016/j.jde.2018.07.076

DO - 10.1016/j.jde.2018.07.076

M3 - Article

AN - SCOPUS:85050886361

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SP - 1313

EP - 1337

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2-3

ER -

Strong transitivity properties for operators

Abstract

Keywords

ASJC Scopus subject areas

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