Date of Award
12-1-2016
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
SULLIVAN, MICHAEL
Abstract
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].
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