# Locally equicontinuous dynamical systems

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 2, page 345-361
- ISSN: 0010-1354

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topGlasner, Eli, and Weiss, Benjamin. "Locally equicontinuous dynamical systems." Colloquium Mathematicae 84/85.2 (2000): 345-361. <http://eudml.org/doc/210818>.

@article{Glasner2000,

abstract = {A new class of dynamical systems is defined, the class of “locally equicontinuous systems” (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in $l_\{∞\}(ℤ)$ form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, where WAP is the class of weakly almost periodic systems and AE the class of almost equicontinuous systems. Both of these inclusions are proper. The main result of the paper is to produce a family of examples of LE dynamical systems which are not WAP.},

author = {Glasner, Eli, Weiss, Benjamin},

journal = {Colloquium Mathematicae},

keywords = {almost equicontinuous dynamical systems; weakly almost periodic dynamical systems; equicontinuity point},

language = {eng},

number = {2},

pages = {345-361},

title = {Locally equicontinuous dynamical systems},

url = {http://eudml.org/doc/210818},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Glasner, Eli

AU - Weiss, Benjamin

TI - Locally equicontinuous dynamical systems

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 2

SP - 345

EP - 361

AB - A new class of dynamical systems is defined, the class of “locally equicontinuous systems” (LE). We show that the property LE is inherited by factors as well as subsystems, and is closed under the operations of pointed products and inverse limits. In other words, the locally equicontinuous functions in $l_{∞}(ℤ)$ form a uniformly closed translation invariant subalgebra. We show that WAP ⊂ LE ⊂ AE, where WAP is the class of weakly almost periodic systems and AE the class of almost equicontinuous systems. Both of these inclusions are proper. The main result of the paper is to produce a family of examples of LE dynamical systems which are not WAP.

LA - eng

KW - almost equicontinuous dynamical systems; weakly almost periodic dynamical systems; equicontinuity point

UR - http://eudml.org/doc/210818

ER -

## References

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