Stephen Haas

Harvey Mudd College Mathematics 2003

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Thesis Proposal: The Hausdorff Dimension of the Julia Set of Polynomials of the Form z^d+c
Thesis Advisor: Prof. Lesley Ward
Second Reader: Prof. Henry Krieger

The Hausdorff Dimension of the Julia Set of Polynomials of the Form z^d+c

In recent years there has been a fair amount of research about the Hausdorff dimension of Julia sets. Among the most interesting is whether the dimension of the Julia set varies continuously with the polynomial generating it. We examine this problem and give a near-complete characterization of the answer for polynomials of the form z^d+c.

Read the final thesis (PDF).

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