Date of Award
8-1-2023
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Sullivan, Michael
Abstract
A template is a key tool that we use to study knotted periodic orbits in the three-dimensional flow. The simplest type of template is the Lorenz template. In [5], Birman and Williams studied knotted periodic orbits with the aid of the Lorenz template. They discovered remarkable properties of Lorenz knots and links. No half twists exist in the Lorenz template. The new template is referred to be a Lorenz-like template when we add half twists. We looked at the template L(1,-1) in this paper, which has a positive half twist on the left-side and a negative half twist on the right. We look for the different types of knots and links that the template contains. Afterward, it was discovered that some knot types in L(1,-1) are fibered. Additionally, we look into the linking number of links in L(1,-1), as well as L(m; n) for m > 0 and n < 0. We have also explored the subtemplate of L(1,-1).
Access
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