Multi-invariant sets on tori

Daniel Berend

doi:10.1090/S0002-9947-1983-0716835-6

Multi-invariant sets on tori

Daniel Berend

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

65 Scopus citations

Abstract

Given a compact metric group G, we are interested in those semigroups ∑of continuous endomorphisms of G, possessing the following property: The only infinite, closed, ∑-invariant subset of G is G itself. Generalizing a one-dimensional result of Furstenberg, we give here a full characterization—for the case of finitedimensional tori—of those commutative semigroups with the aforementioned property.

Original language	English
Pages (from-to)	509-532
Number of pages	24
Journal	Transactions of the American Mathematical Society
Volume	280
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1983-0716835-6
State	Published - 1 Jan 1983
Externally published	Yes

Keywords

Ergodic endomorphism
Finite-dimensional torus
Invariant set
Minimal set
Semigroup of endomorphisms

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9947-1983-0716835-6

Cite this

@article{9f88a21995c646c2af4dd648e089e763,

title = "Multi-invariant sets on tori",

abstract = "Given a compact metric group G, we are interested in those semigroups ∑of continuous endomorphisms of G, possessing the following property: The only infinite, closed, ∑-invariant subset of G is G itself. Generalizing a one-dimensional result of Furstenberg, we give here a full characterization—for the case of finitedimensional tori—of those commutative semigroups with the aforementioned property.",

keywords = "Ergodic endomorphism, Finite-dimensional torus, Invariant set, Minimal set, Semigroup of endomorphisms",

author = "Daniel Berend",

year = "1983",

month = jan,

day = "1",

doi = "10.1090/S0002-9947-1983-0716835-6",

language = "English",

volume = "280",

pages = "509--532",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "2",

}

TY - JOUR

T1 - Multi-invariant sets on tori

AU - Berend, Daniel

PY - 1983/1/1

Y1 - 1983/1/1

N2 - Given a compact metric group G, we are interested in those semigroups ∑of continuous endomorphisms of G, possessing the following property: The only infinite, closed, ∑-invariant subset of G is G itself. Generalizing a one-dimensional result of Furstenberg, we give here a full characterization—for the case of finitedimensional tori—of those commutative semigroups with the aforementioned property.

AB - Given a compact metric group G, we are interested in those semigroups ∑of continuous endomorphisms of G, possessing the following property: The only infinite, closed, ∑-invariant subset of G is G itself. Generalizing a one-dimensional result of Furstenberg, we give here a full characterization—for the case of finitedimensional tori—of those commutative semigroups with the aforementioned property.

KW - Ergodic endomorphism

KW - Finite-dimensional torus

KW - Invariant set

KW - Minimal set

KW - Semigroup of endomorphisms

UR - http://www.scopus.com/inward/record.url?scp=84967780444&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1983-0716835-6

DO - 10.1090/S0002-9947-1983-0716835-6

M3 - Article

AN - SCOPUS:84967780444

SN - 0002-9947

VL - 280

SP - 509

EP - 532

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 2

ER -

Multi-invariant sets on tori

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this