Dynamical systems
Dynamical systems, omega-limit set
Theory of dynamical systems can be understood as an abstract approach to study behavior of solutions that generalizes e.g. qualitative analysis or stability theory. We will focus on asymptotic behavior (behavior for time approaching infinity) of solutions.La Salle's invariance principle
The first application of the theory is La Salle's invariance principle. This approach often allows to prove asymptotic stability where simpler methods (linearization of Lyapunov functions) fail.The Poincaré-Bendixson theory
In a special (but important) case of planar dynamical systems one can take advantage of the topological properties of R2. We will focus on existence of periodic solutions.The whole chapter is here:
