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