Dynamical Properties of Weierstrass Elliptic Functions on Square Lattices

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  • March 21, 2019
Creator
  • Clemons, Joshua J.
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • In this dissertation we prove that the Julia set of a Weierstrass elliptic function on a square lattice is connected. We further show that the parameter space contains an infinite number of Mandelbrot sets. As a consequence, this proves the existence of Siegel disks and gives a description of the bifurcation locus about super-attracting parameters corresponding to super-attracting fixed points. We conclude with a description of a family of rational maps that approximate the Weierstrass elliptic function on a square lattice.
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  • In Copyright
Advisor
  • Hawkins, Jane
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  • Open access
Date uploaded
  • October 11, 2010

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