On dynamics of quadratic maps over finite fields of characteristic two
5
Issued Date
2024
Copyright Date
2019
Language
eng
File Type
application/pdf
No. of Pages/File Size
xi, 62 leaves : ill.
Access Rights
open access
Rights Holder(s)
Mahidol University
Bibliographic Citation
Thesis (Ph.D. (Mathematics))--Mahidol University, 2019
Suggested Citation
Atsanon Wadsanthat On dynamics of quadratic maps over finite fields of characteristic two. Thesis (Ph.D. (Mathematics))--Mahidol University, 2019. Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/91637
Title
On dynamics of quadratic maps over finite fields of characteristic two
Author(s)
Abstract
Quadratic functions defined over finite fields of characteristic two are studied as discrete dynamical systems, especially in terms of classification, nonperiodic points, periodic points, and conjugacy. These functions are organized according to linearity their distinguished elements are counted, and their similarities are considered. By conjugacy and linearity, quadratic functions are categorized into three one-parameter families. One consists of linear transformations, another of affine ones, and the last a single map. The linear transformations are studied by constructing a basis for the underlying field, allowing their non-periodic and periodic points to be described. The affine transformations are associated with linear ones, characterizing their distinguished points. The special points of the remaining map are shown to depend solely on the size of the finite field. Finally, equivalence between maps in each family is given.
Description
Mathematics (Mahidol University 2019)
Degree Name
Doctor of Philosophy
Degree Level
Doctoral Degree
Degree Department
Mahidol University. Faculty of Science
Degree Discipline
Mathematics
Degree Grantor(s)
Mahidol University