Jorge Mozo Fernández
Summary: The idea of this course is to give an introduction to the theory of real dynamical systems from scratch, focusing on the main elements of qualitative theory: equilibria, periodic orbits, limit cycles, … An outline of the contents is as follows:
- Systems of differential equations: existence and uniqueness theorems.
- Dynamical systems. Phase spaces. Classical examples: Logistic equations, predator – prey systems, Lotka- Volterra, …
- Linear dynamical systems. Types of equilibria.
- Non-linear dynamical systems. Topological and analytic equivalence of singular points.
- Stability. Lyapunov functions.
- Periodic solutions. Poincaré-Bendixon Theorem. Stability of periodic orbits. Limit cycles.
- Applications.