On devaney chaos and dense periodic points: Period 3 and Higher implies chaos

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Abstract

We look at density of periodic points and Devaney Chaos. We prove that if f is Devaney Chaotic on a compact metric space with no isolated points, then the set of points with prime period at least n is dense for each n. Conversely, we show that if f is a continuous function from a closed interval to itself, for which the set of points with prime period at least n is dense for each n, then there is a decomposition of the interval into closed subintervals on which either f or f 2 is Devaney Chaotic. (In fact, this result holds if the set of points with prime period at least 3 is dense.).

Original languageEnglish
Pages (from-to)773-780
Number of pages8
JournalAmerican Mathematical Monthly
Volume122
Issue number8
DOIs
Publication statusPublished - 2015

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Periodic Points
Set of points
Chaos
Imply
Closed interval
Compact Metric Space
Continuous Function
Decompose
Closed
Interval

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On devaney chaos and dense periodic points : Period 3 and Higher implies chaos. / Che Dzul-Kifli, Syahida; Good, Chris.

In: American Mathematical Monthly, Vol. 122, No. 8, 2015, p. 773-780.

Research output: Contribution to journalArticle

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