Dynamical systems are central in the study of evolutionary problems and they pervade all of the applied mathematics literature for both finite and infinite dimensional systems. Dynamical systems are typically classified into two main categories, in the first case, time is a continuous variable, and the dynamical system under study takes the form of a differential equation; in the second case, time is a discrete variable, and the dynamical system is a difference equation. In this project we plan to study fundamental problems through geometric and numerical analysis of dynamical systems combining both the continuous and discrete points of view.

The research interests include geometric methods for dynamical systems, integrability in fluid dynamics and numerical simulations, geometric integration of mechanical systems, among others. This group is attested by the number of publications in high impact journals, the international funding obtained (ERC starting grant, IRSES, Bilateral projects…) and the training of predoctoral students and postdoctoral researchers. The research program seeks mutual enrichment in the fields of geometric mechanics, dynamical systems, control theory and optimization, geometric integration, field theory and fluid mechanics.