Date of Award


Document Type

Open Access Thesis

Degree Name

Master of Science (MS)


Physics, Applied

First Advisor

Bala Sundaram

Second Advisor

Maxim Olshanii

Third Advisor

Stephen Arnason


A one-dimensional Hamiltonian system can be modeled and understood as a two-dimensional incompressible fluid in phase space. In this sense, the chaotic behavior of one-dimensional time dependent Hamiltonians corresponds to the mixing of two-dimensional fluids. Amey (2012) studied the characteristic values of one such system and found a scaling law governing them. We explain this scaling law as a diffusion process occurring in an elliptical region with very low eccentricity. We prove that for such a scaling law to occur, it is necessary for a vorticity field to be present. Furthermore, we show that a conformal mapping of an incompressible fluid in an annular region to an elliptical region explains these results for any positive eccentricity less than one.