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arXiv · 1904.08543

Geometric limits of Julia sets for sums of power maps and polynomials

Micah Brame·Scott Kaschner
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Abstract

For maps of one complex variable, $f$, given as the sum of a degree $n$ power map and a degree $d$ polynomial, we provide necessary and sufficient conditions that the geometric limit as $n$ approaches infinity of the set of points that remain bounded under iteration by $f$ is the closed unit disk or the unit circle. We also provide a general description, for many cases, of the limiting set.

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Micah Brame, Scott Kaschner. 2019-04-18. Geometric limits of Julia sets for sums of power maps and polynomials. https://arxiv.org/abs/1904.08543

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