Geometric and numerical analysis of dynamical systems and applications to mathematical physics

Principal Investigator: David Martín de Diego


Geonuma Website


Research Members:

María Barbero Liñán

Manuel de León Rodríguez

Alejandro Luque Jiménez

David Hartley

Ernesto Miguel Nungesser Luengo

Miguel Vaquero Vallina

Marcelo Epstein

Anthony M. Bloch

William Thomas Mark Irvine

Daniel Peralta Salas

Cristina Sardón Muñoz


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 topics to study include geometric methods for dynamical systems, integrability in fluid dynamics and numerical simulations, geometric integration of mechanical systems, among others. The proposed topics have been chosen due to their mathematical relevance and additionally to encourage the collaborative research between all the members of the team. The project is a natural continuation of the outstanding cooperation and research developed by the group members as it 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 and the list of participants have been prepared seeking mutual enrichment in the fields of geometric mechanics, dynamical systems, control theory and optimization, geometric integration, field theory and fluid mechanics.