Grup de recerca consolidat reconegut i finançat

Abstract:

One of the most important aspects of dynamical systems is that they constitute one of the best tools for understanding qualitative and quantitative mathematical models of experimental sciences, physics, chemistry, economics,... Most are modelled by continuous dynamical systems (or differential equations) or discrete dynamical systems (iteration of a function or application).

The objectives of this project are to advance the understanding these systems with emphasis on the study of the following three main topics of research. The first two issues are on continuous dynamic systems, and the third on discrete dynamical systems.

The first issue is the qualitative study of systems of differential equations, with special emphasis on periodic solutions, the number, and its stability, in addition to the integrability of these systems.

The second issue is to study the families of periodic orbits of Hamiltonian systems, with special emphasis on celestial mechanics, and in particular the central configurations of n-body problem.

The third issue we wish to characterize the dynamics, especially the dynamics of different classes of periodic functions.In particular the set of periods of a given map and the kneading theory.