A ZETA FUNCTION FOR FLOWS WITH L(−1,−1) TEMPLATE

In this dissertation, we study the flows on R3 associated with a nonlinear system differential equation introduced by Clark Robinson in [46]. The periodic orbits are modeled by a semi-flow on the L(−1,−1) template. It is known that these are positive knots, but need not have positive braid presentations. Here we prove that they are fibered. We investigate their linking and we construct a zeta-function that counts periodic orbits according to their twisting. This extends work by M. Sullivan in [55], and [57].

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Campus Only Dissertation

Discipline thesis:degree_discipline

Mathematics

Year

2016

Author dc:creator

• AL-Hashimi, Ghazwan Mohammed

Contributors dc:contributor

• SULLIVAN, MICHAEL

• Alexander polynomial of knots
• Fibered Knots
• Lorenz Template and Lorenz-like templates
• Positive knots and positive braids
• Smale Flows
• Zeta function

Repository record dc:identifier

https://opensiuc.lib.siu.edu/dissertations/1291

OAI identifier oai:identifier

oai:opensiuc.lib.siu.edu:dissertations-2295