Teoria qualitativa dels sistemes dinàmics amb èmfasi en les òrbites periòdiques

Dynamical systems are one of the best tools for the qualitative and quantitative understanding of the mathematical models of the experimental sciences. Almost all of them can be formulated by iterating functions (discrete dynamical systems), or by using differential equations (continuous dynamical systems). The goal of this project is the progress in the knowledge of the dynamical systems in the three following main lines: Discrete dynamical systems: (a) Analysis of the complexity of continuous maps of a graph into itself and of continuous maps of a compact period manifold into itself, through their periodic structure, topological entropy, Lefschetz and Nielsen numbers. Continuous dynamical systems: (b) Qualitative study of the global phase portraits of polynomial vector fields puting special attenttion to their limit cycles. (c) Description of the global flow of some restricted three body problems. Central configuration in Celestial Mechanics.