Approximation of fractals generated by Fredholm integral equations
We present the first results of a program recently initiated by us whose main aim is the study of fractals generated by iterated function systems in infinite dimensional spaces (e.g. function spaces). The aim of this paper is to present an example of a fractal, generated by Hutchinson's procedure, embedded in an infinite dimensional Banach space and its finite dimensional approximations. Up to now, the initial finite system of contractions has been given in an Euclidian (finite dimensional) space. Our approach is quite different. Namely, we work in the Banach spare of real valued continuous functions on a compact interval and we describe the attractor generated by an iterated function system given by Fredholm integral equations.
approximation fractals fredholm integral equations iterated function systems function spaces