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Fall 2002 Lifting of almost periodicity of a point through morphisms of flows
Alica Miller
Illinois J. Math. 46(3): 841-855 (Fall 2002). DOI: 10.1215/ijm/1258130988

Abstract

Let $f:\mathcal{X}\rightarrow \mathcal{Y}$ be a morphism of flows, $y$ an almost periodic point of $\mathcal{Y}$, and $x\in f^{-1}(y)$. In general $x$ is not ne\-cessa\-rily almost periodic, but several conditions are known under which that happens. They fall into either ``compact" or ``noncompact" conditions, depending on whether $\mathcal{X}$ and $\mathcal{Y}$ are assumed to be compact or not. In ``noncompact" conditions other assumptions are restrictive. We find a criterion for almost periodicity of $x$, which generalizes both ``compact" and ``noncompact" statements at the same time. We deduce theorems of Ellis, Markley, Kutaibi-Rhodes and Pestov as corollaries.

Citation

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Alica Miller. "Lifting of almost periodicity of a point through morphisms of flows." Illinois J. Math. 46 (3) 841 - 855, Fall 2002. https://doi.org/10.1215/ijm/1258130988

Information

Published: Fall 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1027.37004
MathSciNet: MR1951244
Digital Object Identifier: 10.1215/ijm/1258130988

Subjects:
Primary: ‎37B05‎
Secondary: 54H20‎

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 3 • Fall 2002
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