Research lines:

• Discrete dynamical systems: approximate aggregation of two-time scales systems. We look for conditions allowing us to reduce the dimension of the two-time scales system by translating the fast dynamics to the time scale of the slow dynamics. The interest lies in determining what dynamic information from the reduced system holds (and in what terms) for the original system.

• Hamiltonian systems: chaos and regularity, analytical and numerical techniques for studying the geometry of phase space. Dissipative systems and attractors. Bifurcation theory. 

• Numerical analysis: approximation theory and Lanczos Tau-type spectral methods and the method of alternating projections. 

• Applications: Mathematical modelling in Geophysics, Physics-Mathematics and Chemistry. Population dynamics, species competition, eco-epidemiology, and epidemiology.

Services

• Real-time dynamical analysis of spills or other pollutants in the ocean or the atmosphere.

• Planning ocean glider routes using the geometry of ocean currents.