The first part of the course concerns autonomous and non-autonomous ordinary differential equations, especially those with periodic coefficients, and the associated dynamic systems. Furthermore, abstract dynamic systems (in metric spaces) and their topological properties (limit sets, orbits, recurrence properties) will be introduced. Some fundamental arguments will also be presented from the application point of view, such as the theory of stability and invariant sets. The second part of the course concerns the introduction of some topological methods in nonlinear analysis, such as the theory of fixed points in finite dimension and infinite dimension and on manifolds, with different applications to non-linear problems. Finally, in the final part of the course some applications of the developed methods will be proposed and some current research fields will be indicated where these methods are used, including the issues related to “deterministic chaos” and complex systems.

At the request of the students, the course can be held in English.