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

70 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

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10.1090/S0002-9947-1983-0716835-6

Cite this

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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 - https://www.scopus.com/pages/publications/84967780444

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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

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