Dynamics of an Analogue of the Quadratic Family on Su (2)

Date of Award

2010

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Keywords

Quadratic Family, Dynamical Systems, Chaos

Area of Concentration

Mathematics

Abstract

For this thesis an analogue of the well known Quadratic Family was constructed for S3, the unit sphere in R4, using the algebra of unit quaternions. Because the unit quaternions can be identified with the Lie group SU(2), the family provides a collection of dynamical systems on SU(2). These dynamics for SU(2) were analyzed with the purpose of finding analogues of the well-known phenomenon associated to the Quadratic Family. This was accomplished by computing the orbits of many different seed values for different parameter values and then creating a graphical representation of the data. The results indicate that the dynamics on SU(2) are rich and that there are some similarities between it and the quadratic family.

Rights

This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.

This document is currently not available here.

Share

COinS