On the structure of the ω-limit sets for continuous maps of the interval

Lluís Alsedà, Moira Chas, Jaroslav Smítal

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

We introduce the notion of the center of a point for discrete dynamical systems and we study its properties for continuous interval maps. It is known that the Birkhoff center of any such map has depth at most 2. Contrary to this, we show that if a map has positive topological entropy then, for any countable ordinal α, there is a point xα ∈ I such that its center has depth at least α. This improves a result by [Sharkovskii, 1966].
Original languageEnglish
Pages (from-to)1719-1729
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume9
Issue number9
Publication statusPublished - 1 Jan 1999

Fingerprint Dive into the research topics of 'On the structure of the ω-limit sets for continuous maps of the interval'. Together they form a unique fingerprint.

Cite this