Teor\'ia Erg\'odica de los Atractores Topol\'ogicos y Estad\'isticos (Ergodic Theory of Topological and Statistical Attractors) (Spanish)

Abstract

This is a textbook, in Spanish, for an introductory short course that focusses on the ergodic properties of topological and statistical attractors. It is directed to graduate students in Mathematics and related Science, in particular to the students-participants of the XXVI Escuela Venezolana de Matem\'atica. The first three chapters include a review of the basic concepts and properties of the ergodic theory and of the topological and differentiable dynamics of systems that evolve on discrete time. They do not require from the reader previous knowledge on Dynamical Systems. The latter three chapters develop the theory of topological attractors, SRB measures, and the existence of Gibbs and physical measures for hyperbolic and sufficiently differentiable systems. Finally, for continuous and non necessarily differentiable systems, we include a review of Milnor's and Ilyashenko's or statistical attractors, the proof of their existence and the relation between statistical attractors and the "SRB-like" or pseudo-physical measures.