Mathematics and Computer Applications - Sciene

Planar noninvertible maps have been studied recently by several authors such as Mira [32], Gardini [17], and Cathala [9], much of their work has been concentrated on analyzing some examples and making some conclusions on the properties of the maps.
     The main purpose of this thesis can be divided into three objectives:
First objective: introduce the mathematical background of the main notions and proposition on the theory of the dynamical system. Specifically we shall foucus our study on planar nonivertiable continuously differentiable maps T:

The main purpos of this work can be classified into four objects. These are summarized as follows:

The main aim of this thesis is focused on studying some non-linear uncertain stochastic dynamical system.The necessary background for stochastic process, stochastic integral for Brownian motion and fractional Brownian motion, stochastic dynamical system driven by Brownian motion and fractional Brownian motion are studied and discussed supported by useful comments and examples. Ito Some class of non-linear   stochastic ordinary control system driven by Brownian motion as well as fractional Brownian motion have been considered and discussed.