Dynamical properties of Weierstrass elliptic functions on square lattices |
Posted on:2011-08-15 | Degree:Ph.D | Type:Dissertation |
University:The University of North Carolina at Chapel Hill | Candidate:Clemons, Joshua J | Full Text:PDF |
GTID:1440390002458079 | Subject:Mathematics |
Abstract/Summary: | |
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. |
Keywords/Search Tags: | Weierstrass elliptic function, Square lattice |
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