Linear cocycles as an interface between dynamical systems and mathematical physics

SIlvius Klein (PUC-Rio)

A linear cocycle is a dynamical system on a vector bundle, which preserves the linear bundle structure and induces a measure preserving dynamical system on the base. Important examples of linear cocycles arise in connection with solving the eigenvalue equation of a discrete Schrödinger operator. Studying their statistical properties (such as large deviations), besides being interesting in itself, has applications in dynamics (for instance regarding the regularity of the Lyapunov exponents) and in mathematical physics (for instance in establishing spectral properties such as Anderson localization). The goal of this talk is to explain these connections and to describe some interesting models..