Kirthana Rajasekar: What are Lyapunov exponents?

Abstract

In this talk, an intuition for these exponents is built using the barycentric subdivision of a triangle. The dynamics we observe in the above example, is then described using a more generalized concept of cocyles over a measure preserving dynamical system. Lyapunov exponents will then be formally defined and some of its properties discussed. If time permits, we will also discuss Lyapunov exponents for Schrödinger cocyles.

These topics fall in the area of dynamical systems and ergodic theory, which involves the study of time evolution of certain systems. The long term evolution of a space, even under a simple deterministic map, can be very unpredictable. Lyapunov exponent is a quantity that characterizes the stability of such dynamics.

The talk will be self-contained, with pre-requisites of only basic analysis and measure theory.