Martes 21 de Enero, 11:15, Aula Gris 2, ICMAT

Jaime. J. Sáchez-Gabites (UAM)

Title: An algebraic question motivated by a problem in dynamics

Abstract:  When a dynamical system has an attractor, the latter usually provides interesting information about the dynamics. Most attractors exhibit a rather complex structure which makes describing their full topological type extremely difficult. A more modest goal is to compute some useful topological invariants of the attractor such as (broadly speaking) its homology or homotopy type. This classical problem very often needs to be addressed indirectly, since attractors are not explicitly computable.

In this talk we will first discuss this problem in the case of continuous dynamics (that is, flows), where the solution is very simple. Then we will move on to the discrete case (dynamics generated by the iteration of a homeomorphism), which turns out to be much more complicated. The ultimate goal of the talk is to show how this dynamical problem eventually leads to an algebraic question that seems to have interest on its own.