The Boundedness Locus and baby Mandelbrot sets for some generalized McMullen maps
Suzanne Boyd, Alexander J. Mitchell

TL;DR
This paper investigates the parameter spaces of certain rational functions, revealing embedded Mandelbrot set copies and employing polynomial-like map techniques to analyze their boundedness loci.
Contribution
It extends the understanding of Mandelbrot set embeddings to generalized McMullen maps with fixed degree, using polynomial-like map methods.
Findings
Identified homeomorphic copies of Mandelbrot sets in parameter planes.
Applied Douady-Hubbard techniques to rational functions.
Analyzed boundedness loci for specific parameter ranges.
Abstract
In this paper we study rational functions of the form with fixed and at least , and hold either or fixed while the other varies. We locate some homeomorphic copies of the Mandelbrot set in the -parameter plane for certain ranges of , as well as in the -plane for some -ranges. We use techniques first introduced by Douady and Hubbard, that were applied for the subfamily by Robert Devaney. These techniques involve polynomial-like maps of degree two.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Meromorphic and Entire Functions · Advanced Differential Equations and Dynamical Systems
