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Limits Of Julia Sets For Sums Of Power Maps And Polynomials, Micah Brame
Limits Of Julia Sets For Sums Of Power Maps And Polynomials, Micah Brame
Undergraduate Honors Thesis Collection
Suppose f_{n,c} is a complex-valued mapping of one complex variable given by f_{n,c}(z) = z^n + p(z) + c, where p is a polynomial such that p(0) = 0 and c is a complex parameter such that |c| < 1. 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_{n,c} is the disk of radius 1 centered at the origin.