Date of Award
Open Access Thesis
Master of Science (MS)
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.
Jauffred, Francisco J., "Hydrodynamic Analogues of Hamiltonian Systems" (2015). Graduate Masters Theses. 317.