Please use this identifier to cite or link to this item:

Exceptional Points in Arithmetic Dynamics

File Description SizeFormat 
2015-05-phd-thompson_r.pdfVersion for non-UH users. Copying/Printing is not permitted541.39 kBAdobe PDFView/Open
2015-05-phd-thompson_uh.pdfFor UH users only567.24 kBAdobe PDFView/Open

Item Summary

Title: Exceptional Points in Arithmetic Dynamics
Authors: Thompson, Bianca
Issue Date: May 2015
Publisher: [Honolulu] : [University of Hawaii at Manoa], [May 2015]
Abstract: Let be a morphism of PN defined over a field K. We prove three main results:
When K is a number field, we prove that there is a bound B depending only on such that every twist of has no more than B K-rational preperiodic points. (This result is analagous to a result of Silverman for abelian varieties.) For two specific families of quadratic rational maps over Q, we find the bound B explicitly.
When K is a finite field, we find the limiting proportion of periodic points in towers of finite fields for polynomial maps associated to algebraic groups, namely pure power maps (z) = zd and Chebyshev polynomials.
When K is a number field or Qp for p 6= 3; and L=K is an extension we prove that K fails to be critically reducible at 3. Meanwhile, Q3 is critically reducible at 3.
Description: Ph.D. University of Hawaii at Manoa 2015.
Includes bibliographical references.
Appears in Collections:Ph.D. - Mathematics

Please contact if you need this content in an ADA compliant alternative format.

Items in ScholarSpace are protected by copyright, with all rights reserved, unless otherwise indicated.