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2000/2001 The Essential Point Set of a Continuous Function
T. H. Steele
Real Anal. Exchange 26(1): 201-216 (2000/2001).


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.


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T. H. Steele. "The Essential Point Set of a Continuous Function." Real Anal. Exchange 26 (1) 201 - 216, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 2 January 2009

zbMATH: 1071.26500
MathSciNet: MR1825504

Primary: 26A18 , 54H20‎

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

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 1 • 2000/2001
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