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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/5907

Title: On the Study of Topological Dynamical Systems
Authors: Obeng-Denteh, William
Issue Date: 21-Jun-2012
Abstract: The purpose of the study was to apply Topological Dynamics to Integral Equations. Topo- logical Dynamical techniques were used to analyse it and con rmed the results. Sell de- veloped methods which allowed one to apply the theory of topological dynamics to a very general class of nonautonomous ordinary di erential equations. This was extended to non- linear Volterra's Integral Equations. This research took o from there and applied the techniques of topological dynamics to an integral equation. The usage of limiting equa- tions which were used by Sell on his application to integral equations were extended to recurrent motions and then studied the solution path. It thus con rmed the existence of contraction and the stationary point in the said paper. The study of Dynamical Systems of Shifts in the space of piece-wise continuous functions analogue to the known Bebutov system was embarked upon. The stability in the sense of Poisson discontinuous function was shown. It was proved that a xed discontinuous function, f, is discontinuous for all its shifts, , whereas the trajectory of discontinuous function is not a compact set. The study contributes to literature by providing notions of Topological Dynamic techniques which were used to analyse and con rm the existence and contractions and the stationary points of a special Integral Equation.
Description: A thesis Presented to the Department of Mathematics,Kwame Nkrumah University of Science and Technology in Partial Ful llment of the Requirements for the Degree of Doctor of Philosophy in Pure Mathematics, June-2012
URI: http://hdl.handle.net/123456789/5907
Appears in Collections:College of Science

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