11 
The Dynamics of Inhomogeneous CosmologiesLim, Woei Chet January 2004 (has links)
In this thesis we investigate cosmological models more general than the isotropic and homogeneous FriedmannLemaître models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and the cosmological constant. We formulate the Einstein field equations as a system of quasilinear first order partial differential equations, using scaleinvariant variables. The primary goal is to study the dynamics in the two asymptotic regimes, i. e. near the initial singularity and at late times. We highlight the role of spatially homogeneous dynamics as the background dynamics, and analyze the inhomogeneous aspect of the dynamics. We perform a variety of numerical simulations to support our analysis and to explore new phenomena.

12 
The Dynamics of Inhomogeneous CosmologiesLim, Woei Chet January 2004 (has links)
In this thesis we investigate cosmological models more general than the isotropic and homogeneous FriedmannLemaître models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and the cosmological constant. We formulate the Einstein field equations as a system of quasilinear first order partial differential equations, using scaleinvariant variables. The primary goal is to study the dynamics in the two asymptotic regimes, i. e. near the initial singularity and at late times. We highlight the role of spatially homogeneous dynamics as the background dynamics, and analyze the inhomogeneous aspect of the dynamics. We perform a variety of numerical simulations to support our analysis and to explore new phenomena.

13 
Some aspects of the geometry of Poisson dynamical systemsNarayanan, Vivek. January 2001 (has links)
Thesis (Ph. D.)University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

14 
Control of nonholonomic systemsYuan, Hongliang. January 2009 (has links)
Thesis (Ph.D.)University of Central Florida, 2009. / Adviser: Zhihua Qu. Includes bibliographical references (p. 138143).

15 
Some aspects of the geometry of Poisson dynamical systemsNarayanan, Vivek 30 March 2011 (has links)
Not available / text

16 
ONEPARAMETER OPERATOR SEMIGROUPS AND AN APPLICATION OF DYNAMICAL SYSTEMSAlhulaimi, Bassemah 14 August 2012 (has links)
This thesis consists of two parts. In the first part, which is expository, abstract theory of oneparameter operator is studied semigroups. We develop in detail the necessary Banach space and Banach algebra theories of integration, differentiation, and series, and then give a careful rigorous proof of the exponential function characterization of continuous oneparameter operator semigroups. In the second part, which is applied and has new result, we discuss some related topics in dynamical systems. In general the linearizations give a reliable description of the nonlinear orbits near the equilibrium points (the HartmanGrobman theorem), thus illustrating the importance of linear semigroups. The aim of qualitative analysis of differential equations (DE) is to understand the qualitative behaviour (such as, for example, the longterm behaviour as $t\rightarrow \infty$) of typical solutions of the DE. The flow in the direction of increasing time defines a semigroup. As an application we study EinsteinAether Cosmological models using dynamical systems theory.

17 
A contraction argument for twodimensional spiking neuron modelsFoxall, Eric 16 August 2011 (has links)
The field of mathematical neuroscience is concerned with the modeling and interpretation of neuronal dynamics and associated phenomena. Neurons can be modeled individually, in small groups, or collectively as a large network. Mathematical models of single neurons typically involve either differential equations, discrete maps, or some combination of both. A number of twodimensional spiking neuron models that combine continuous dynamics with an instantaneous reset have been introduced in the literature. The models are capable of reproducing a variety of experimentally observed spiking patterns, and also have the advantage of being mathematically tractable. Here an analysis of the transverse stability of orbits in the phase plane leads to sufficient conditions on the model parameters for regular spiking to occur. The application of this method is illustrated by three examples, taken from existing models in the neuroscience literature. In the first two examples the model has no equilibrium states, and regular spiking follows directly. In the third example there are equilibrium points, and some additional quantitative arguments are given to prove that regular spiking occurs. / Graduate

18 
The control of chaosBird, C. M. January 1996 (has links)
No description available.

19 
Triangular billiards surfaces and translation covers /Schmurr, Jason Peter. January 1900 (has links)
Thesis (Ph. D.)Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 6364). Also available on the World Wide Web.

20 
The Szemerédi property in noncommutative dynamical systemsBeyers, Frederik Johannes Conradie 24 May 2009 (has links)
No abstract available. Copyright 2008, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. Please cite as follows: Beyers, FJC 2008, The Szemerédi property in noncommutative dynamical systems, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd05242009145506/ > D620/ag / Thesis (PhD)University of Pretoria, 2009. / Mathematics and Applied Mathematics / unrestricted

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