Geometrical Theory of Dynamical systems in Invariant Manifolds

Abstract

In this research we consider the problem of the characterization of chaotic dynamics, for this we discuss and analyssis the standard maps by using the perturbative method to study their induced orbits. We discuss the stationary solution and the periodic orbits of dynamical system, and we investigate the Floquent theorem. We also discuss the local Bifurcations in terms of dependent parameter of ordinary differential equations and the dependent parameter maps with some applications. Also we illustrate the characterization of chaotic dynamics briefly by discussing the symbolic dynamics and the strange attractors with some remarks and applications.