Real Analysis Exchange

The Essential Point Set of a Continuous Function

T. H. Steele

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Abstract

For continuous self maps of $[0,1]$, we extend M. K. Fort, Jr.'s notion of an essential fixed point to points generating nonsingleton $\omega $-limit sets. The $\omega $-limit sets of these essential points are, in a metric sense, stable under small perturbations of the function. We develop some of the properties of the essential point set of a continuous function, and investigate the relationship between essential points, $\omega $-limit sets, and the chaotic nature of the generating function.

Article information

Source
Real Anal. Exchange, Volume 26, Number 1 (2000), 201-216.

Dates
First available in Project Euclid: 2 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.rae/1230939154

Mathematical Reviews number (MathSciNet)
MR1825504

Zentralblatt MATH identifier
1071.26500

Subjects
Primary: 54H20: Topological dynamics [See also 28Dxx, 37Bxx] 26A18: Iteration [See also 37Bxx, 37Cxx, 37Exx, 39B12, 47H10, 54H25]

Keywords
essential point recurrent point $\omega $-limit set

Citation

Steele, T. H. The Essential Point Set of a Continuous Function. Real Anal. Exchange 26 (2000), no. 1, 201--216. https://projecteuclid.org/euclid.rae/1230939154


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