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dc.contributor.authorCuzzocreo, Daniel L.en_US
dc.date.accessioned2016-03-08T19:10:29Z
dc.date.available2016-03-08T19:10:29Z
dc.date.issued2014
dc.identifier.urihttps://hdl.handle.net/2144/15115
dc.description.abstractFor parametrized families of dynamical systems, two major goals are classifying the systems up to topological conjugacy, and understanding the structure of the bifurcation locus. The family Fλ = z^n + λ/z^d gives a 1-parameter, n+d degree family of rational maps of the Riemann sphere, which arise as singular perturbations of the polynomial z^n. This work presents several results related to these goals for the family Fλ, particularly regarding a structure of "necklaces" in the λ parameter plane. This structure consists of infinitely many simple closed curves which surround the origin, and which contain postcritically finite parameters of two types: superstable parameters and escape time Sierpinski parameters. First, we derive a dynamical invariant to distinguish the conjugacy classes among the superstable parameters on a given necklace, and to count the number of conjugacy classes. Second, we prove the existence of a deeper fractal system of "subnecklaces," wherein the escape time Sierpinski parameters on the previously known necklaces are themselves surrounded by infinitely many necklaces.en_US
dc.language.isoen_US
dc.subjectMathematicsen_US
dc.subjectComplex dynamicsen_US
dc.subjectDynamical systemsen_US
dc.titleDynamical invariants and parameter space structures for rational mapsen_US
dc.typeThesis/Dissertationen_US
dc.date.updated2016-01-22T18:58:56Z
etd.degree.nameDoctor of Philosophyen_US
etd.degree.leveldoctoralen_US
etd.degree.disciplineMathematics & Statisticsen_US
etd.degree.grantorBoston Universityen_US


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