The qualitative theory of differential equations studies the behavior of differential equations by means other than the search for their solutions. It started with the works of Henri Poincaré and Aleksandr Lyapunov. Relatively few differential equations can be solved explicitly, but using analysis and topology tools, they can be "solved" in a qualitative sense, obtaining information about their properties. Among others, the main interests in this field are the study of structural stability, bifurcations, integrability, the existence and number of periodic orbits, homoclinic and heteroclinical connections. This school will be structured in five mini-courses of 6 hours each in which the classic techniques for the study of some of the aforementioned concepts will be presented. In each course, we will show the similarities and differences between smooth and non-smooth differential systems.

The summer school is supported by the European RISE project Dynamics (H2020-MSCA-RISE-2017 - 777911, http://www.gsd.uab.cat/dynamicsh2020/) and Grup de Sistemes Dinàmics de la UAB (http://www.gsd.uab.cat)

Mini-Courses

1. Structural stability and bifurcations of low codimension in piecewise differential systems, Tiago de Carvalo (Universidade de Sao Paulo)

2. Integrability and limit cycles in piecewise differential systems, Jaume Llibre (Universitat Autònoma de Barcelona)

3. The averaging method, Douglas D. Novaes (Universidade Estadual de Campinas)

4. Bifurcation Analysis in Piecewise Linear Systems, Enrique Ponce (Universidad de Sevilla)

5. Center-focus and cyclicity problems, Joan Torregrosa (Universitat Autònoma de Barcelona)