About Stable and Unstable Sets

Abstract

First of all, a simplified study of stable and unstable sets is presented, with special mention of manifolds. In the first chapter, we dealt with definitions and basic characteristics and the most important thing it was the classification of the manifolds, where we classified them into three types: the stable manifold, the unstable manifold, and the central manifold. In the second chapter, we examined the phenomenon of chaos through the boost converter in equations of a certain shape. We carefully analyzed complex behavior in several parameters and then finally arrived at the case in which robust chaos occurs. In the third chapter, we attached great importance to stability theories with Lyapunov’s concept, and then expanded to the LaSalle’s principle. We also passed instability theories. We point out that we have annotated most of the definitions and theories with several examples that enabled us to identify the importance of these theories in our practical life.