Skip navigation
Please use this identifier to cite or link to this item:
Title: Finite Orbits of a Polynomial Automorphism on Ane Three Space with Applications
Authors: Yang, Daphne
Advisors: Sarnak, Peter
Skinner, Chris
Department: Mathematics
Class Year: 2018
Abstract: In the PainlevĀ“e VI differential equation, a certain group action governs the behavior of solutions as they are analytically continued around a pole. It turns out that the finite groups correspond to the algebraic solutions. In this paper, we will study the finite groups of this action in affine three-space. A complete classification of all finite orbits will be done in a single-parameter case, and an overview of the classification for a more complex case will also be studied. Remarkably, there is a deep connection between these finite orbits and the transitivity of another action in a Diophantine equation. We will investigate how classifying the finite orbits will give obstructions to the action being transitive in a finite field.
Type of Material: Princeton University Senior Theses
Language: en
Appears in Collections:Mathematics, 1934-2020

Files in This Item:
File SizeFormat 
YANG-DAPHNE-THESIS.pdf390.67 kBAdobe PDF    Request a copy

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