dc.contributor.author | Alhulaimi, Bassemah | |
dc.date.accessioned | 2012-08-28T12:33:58Z | |
dc.date.available | 2012-08-28T12:33:58Z | |
dc.date.issued | 2012-08-28 | |
dc.identifier.uri | http://hdl.handle.net/10222/15391 | |
dc.description.abstract | This thesis consists of two parts. In the first part, which is expository, abstract theory of one-parameter operator is studied semi-groups. 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 one-parameter 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 non-linear orbits near the equilibrium points (the Hartman-Grobman 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 long-term 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 Einstein-Aether Cosmological models using dynamical systems theory. | en_US |
dc.language.iso | en | en_US |
dc.subject | SEMIGROUPS AND DYNAMICAL SYSTEMS | en_US |
dc.title | ONE-PARAMETER OPERATOR SEMIGROUPS AND AN APPLICATION OF DYNAMICAL SYSTEMS | en_US |
dc.date.defence | 2012-08-14 | |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.degree | Master of Science | en_US |
dc.contributor.external-examiner | na | en_US |
dc.contributor.graduate-coordinator | Keith Johnson | en_US |
dc.contributor.thesis-reader | Iron David | en_US |
dc.contributor.thesis-supervisor | Fraser Andrea, and Coley Alan | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.manuscripts | Not Applicable | en_US |
dc.contributor.copyright-release | Not Applicable | en_US |