Résumé:
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.
