Abstract
An iterated function system (IFS) on a compact metric space is a finite collection of mappings of the space into itself. Under suitable conditions, an attractor for the IFS can be defined in a natural way. If the mappings depend on a parameter, the subset of the parameter space for wich the corresponding attractor is connected is called the Mandelbrot set of the family. Under some suitable symmetry conditions, it can be shown that, for parameter values not in the Mandelbrot set, the attractor is homeomorphic to the Cantor set. We determine the Mandelbrot set for a family of nonlinear IFS’s on the unit triangle obtained from the problem of filtering the noise from a Markov chain signal model.
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