Multi-invariant sets on compact abelian groups

Daniel Berend

doi:10.1090/S0002-9947-1984-0760973-X

Multi-invariant sets on compact abelian groups

Daniel Berend

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

33 Scopus citations

Abstract

Let G be a finite-dimensional connected compact abelian group. Generalizing previous results, dealing with the case of finite-dimensional tori, a full characterization is given herewith of those commutative semigroups 2 of continuous endomorphisms Σ of G which satisfy the following property: The only infinite closed Σ-invariant subset of G is G itself.

Original language	English
Pages (from-to)	505-535
Number of pages	31
Journal	Transactions of the American Mathematical Society
Volume	286
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1984-0760973-X
State	Published - 1 Jan 1984
Externally published	Yes

Keywords

Ergodic endomorphism
Finite-dimensional group
Invariant set
Minimal flow
Multi-parameter flow
Semigroup of endomorphisms
Solenoid

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9947-1984-0760973-X

Cite this

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AB - Let G be a finite-dimensional connected compact abelian group. Generalizing previous results, dealing with the case of finite-dimensional tori, a full characterization is given herewith of those commutative semigroups 2 of continuous endomorphisms Σ of G which satisfy the following property: The only infinite closed Σ-invariant subset of G is G itself.

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KW - Finite-dimensional group

KW - Invariant set

KW - Minimal flow

KW - Multi-parameter flow

KW - Semigroup of endomorphisms

KW - Solenoid

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Multi-invariant sets on compact abelian groups

Abstract

Keywords

ASJC Scopus subject areas

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