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 some classes of functions in dimension one and greater than one through their periodic structure and topological entropy. Continuous dynamical systems: b) qualitative study of the global phase portraits of systems of polynomial differential equations; c) qualitative theory of some restricted three and four body problems in celestial mechanics.
|Effective start/end date||27/06/94 → 17/06/97|