Center Manifolds Theorem and Applications to Dynamical Systems

Abstract

In this research we consider the most useful methods to study the flow near bifurcation point, that is the center manifolds theorem. Because of this way study the Dynamical Systems and there geometrical theory with some examples. Also we discuss the basic concepts of studying dynamical system with some applications. We discuss the stationary and periodic solutions and we illustrate how to determine relations between linear or nonlinear stability. Also we study the center manifolds and their prosperities. We discuss the bifurcations involving a single or several eigenvalues with some applications and examples.