PRE2023-GEOMETRIA DE SISTEMAS DINAMICOS: DE LA TEORIA A LAS APLICACIONES-PID2022-137909NB-C21

GEOMETRY OF DYNAMICAL SYSTEMS: FROM THEORY TO APPLICATIONS The proposal belongs to the area of mathematics as it is focused on developing relevant aspects of the geometry of dynamical systems and applications. Dynamical systems are the core of evolutionary problems and pervade the entire literature in applied mathematics for both finite and infinite dimensional systems and from continuous to discrete evolution. Dynamical systems are typically classified into two main categories. In the first case, time is a continuous variable and the dynamical system under study is described by differential equations. In the second case, time is a discrete variable and the dynamical system is described by difference equations. In this project we plan to study fundamental problems on geometric and numerical analysis of dynamical systems that require the combination of the continuous and discrete points of view in order to tackle problems with impact in the real-world. Thus, our interdisciplinary proposal clearly fits into the area of Geometric Mechanics using techniques of Differential Geometry, Applied Mathematics and Mathematical Physics. It goes beyond theoretical developments, by including relevant applications to Engineering.