Browsing by Author "Obeng-Denteh, William"

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    On the Study of Topological Dynamical Systems
    (June 2012 ) Obeng-Denteh, William
    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.
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    Using the Logistic Map as Compared to the Cubic Map to Show the Convergence and the Relaxation of the Period–1 Fixed Point
    (Hindawi, 2022-07) Asamoah, Joshua Kiddy K.; Mensah, Patrick Akwasi Anamuah; Obeng-Denteh, William; Issaka, Ibrahim; Gyamfi, Kwasi Baah; 0000-0002-7066-246X
    point of a system, speci cally, the period—1 xed point. e study has shown that the period—1 xed point of a logistic map as a recurrence has its convergence at a transcritical bifurcation having its power-law t with exponent ­ − 1 when 1 and 0. e cubic map shows its convergence to the xed point at a pitchfork bifurcation decaying at a power law with exponent ­ − (1/2) 1 and 0. However, the system shows their relaxation time at the same power law with exponents and z − 1.