Belyi Maps and Bicritical Polynomials

dc.contributor.advisor	Manes, Michelle
dc.contributor.author	Tobin, Isabella Olympia
dc.contributor.department	Mathematics
dc.date.accessioned	2019-10-09T18:54:49Z
dc.date.available	2019-10-09T18:54:49Z
dc.date.issued	2019
dc.description.degree	Ph.D.
dc.identifier.uri	http://hdl.handle.net/10125/63502
dc.subject	Mathematics
dc.subject	Arithmetic Dynamics
dc.subject	Number Theory
dc.title	Belyi Maps and Bicritical Polynomials
dc.type	Thesis
dcterms.abstract	Let $K$ be a number field. We will show that any bicritical polynomial $f(z) \in K[z]$ is conjugate to a polynomial of the form $a\mathcal{B}_{d,k}(z) +c \in \bar{K}[z]$ where $\mathcal{B}_{d,k}(z)$ is a normalized single-cycle Belyi map with combinatorial type $(d; d-k, k+1, d)$. We use results of Ingram \cite{ingram2010} to determine height bounds on pairs $(a,c)$ such that $a\mathcal{B}_{d,k}(z) +c$ is post-critically finite. Using these height bounds, we completely describe the set of post-critically finite cubic polynomials of the form $a\mathcal{B}_{d,k}(z)+c \in \mathbb{Q}[z]$, up to conjugacy over $\mathbb{Q}$. We give partial results for post-critically finite polynomials over $\mathbb{Q}$ of arbitrary degree $d>3$.
dcterms.extent	65 pages
dcterms.language	eng
dcterms.publisher	University of Hawai'i at Manoa
dcterms.type	Text
local.identifier.alturi	http://dissertations.umi.com/hawii:10389

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