On the structure of transitive \(\omega\)-limit sets for continuous maps
type: Item
instance of: scholarly article
title: On the structure of transitive \(\omega\)-limit sets for continuous maps
zbMATH Open document ID: 1057.37007
DOI: 10.1007/BF02972825
author: Andrei G. Sivak
published in: Qualitative Theory of Dynamical Systems
publication date: 2004-06-09T00:00:00Z
review text: The goal of this paper is to discuss the admissible topological structure of \(\omega\)-limit sets for continuous maps on compact metric spaces. The author considers the problem from continuum theory point of view and describes the admissible topological structure of \(\omega\)-limit sets using the notion of arc component of a set. It is proved that for a complete characterization of \(\omega\)-limit sets in terms of arc components, one should take into account not only the number of arc components and their intersections but also the way in which convergence continua in the set are approximated.
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 2071091
zbMATH Keywords: continuous map
zbMATH Keywords: topological structure
zbMATH Keywords: \(\omega\)-limit set
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2071091