DYNAMICAL SYSTEMS EVOLVING

Abstract

This is an expanded version of a presentation given at ICM2018. It discusses a number of results taken from a cross-section of the author’s work in Dynamical Systems. The topics include relation between entropy, Lyapunov exponents and fractal dimension, statistical properties of chaotic dynamical systems, physically relevant invariant measures, strange attractors arising from shearinduced chaos, random maps and random attractors. The last section contains two applications of Dynamical Systems ideas to Biology, one to epidemics control and the other to computational neuroscience.