SIPo: The regularity of the Lyapunov exponents

Abstract: 

Dynamical systems are an area of mathematics that studies how processes evolve over time. One of the main perspectives within this field is Ergodic Theory, which studies dynamical systems from the point of view of measure theory. Within ergodic theory, one of the main elements of study currently is the Lyapunov exponents.

Lyapunov exponents quantify the dependence of the system on its initial conditions. One of the central problems regarding Lyapunov exponents is the study of their continuity, that is, to understand how much the Lyapunov exponents change under small perturbations of the system’s parameters. This question is important because it allows us to better understand the behavior of dynamical systems with close parameters.

In this talk, we will introduce the concepts of Lyapunov exponents, dynamical systems, and linear cocycles. We will also discuss the possibility of obtaining continuity results and moduli of continuity for Lyapunov exponents in certain classes of dynamical systems.

Speaker: Aline Melo (PUCV)