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Qualitative Behavior Of Dynamical Vector Fields

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Qualitative Behavior Of Dynamical Vector Fields

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dc.contributor.author Kirby, Roger Dale en_US
dc.date.accessioned 2007-09-17T17:07:34Z
dc.date.available 2007-09-17T17:07:34Z
dc.date.issued 2007-09-17T17:07:34Z
dc.date.submitted August 2007 en_US
dc.identifier.other DISS-1829 en_US
dc.identifier.uri http://hdl.handle.net/10106/617
dc.description.abstract Differential Equations come in two classes, deterministic and stochastic. The first part of this analysis establishes the stable properties of the set of all trajectories converging on a critical point in the real plane defined by two distinct negative eigenvalues. Also in the deterministic class I offer a method for finding closed-form primitives for a great variety of differential forms, through a reduction process facilitated by a Lyapunov-type Energy function. Many of these forms lie in classes which heretofore have not been shown to be solvable in closed form. The last part of this work outlines the appropriate procedures for calculating differentials and solutions for fields perturbed by random processes . In the final chapter a new theory of Laplace Transforms for stochastic calculations has been developed. The introduction of a Table of Transforms has been initiated, and shall eventually be enlarged. Applications are offered to demonstrate its utility. en_US
dc.description.sponsorship Ladde, Gangaram en_US
dc.language.iso EN en_US
dc.publisher Mathematics en_US
dc.title Qualitative Behavior Of Dynamical Vector Fields en_US
dc.type Ph.D. en_US
dc.contributor.committeeChair Ladde, Gangaram en_US
dc.degree.department Mathematics en_US
dc.degree.discipline Mathematics en_US
dc.degree.grantor University of Texas at Arlington en_US
dc.degree.level doctoral en_US
dc.degree.name Ph.D. en_US

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