Grup de recerca consolidat reconegut

Abstract:

Dynamical Systems is the area of mathematics studying the asymptotic behaviour of some given bodies or agents under the action of a set of forces or rules. By bodies or agents we mean either points in an abstract topological space (e.g. an n-dimensional manifold, open or closed, with or without boundary, with low, high or even infinite dimension, etc), or more concrete elements of natural or social sciences (e.g. motion of celestial bodies, prices of goods in the economy, drugs in blood, animals or trees in forests, infected patients in a certain population, etc). The possibility of having these two different points of view is a natural link between pure mathematics, applied mathematics and other disciplines of science. In particular, this project combines different approaches to research in Dynamical Systems including topological, analytical, numerical and qualitative methods, aiming not only to move forward and to search excellence in each one of them but also to make use of possible synergies among them.

We focus our attention on dynamical systems defined either by iteration of continuous, differentiable or holomorphic maps (so called discrete dynamical systems), or by the solutions of differential equations (so called continuous dynamical systems), both in a low dimensional framework, and applications of these techniques to other sciences. Precisely, we consider real and complex dynamical systems using topological, analytical, numerical and qualitative tools among others. With this aim, we take a theoretical approach as well as a numerical one, developing algorithms to give quantitative answers.