What are Lyapunov exponents, and why are they interesting?
arXiv:1608.02843
Abstract
This expository paper, based on a Current Events Bulletin talk at the January, 2016 Joint Meetings, introduces the concept of Lyapunov exponents and discusses the role they play in three areas: smooth ergodic theory, Teichmüller theory, and the spectral theory of one-frequency Schrödinger operators. The inspiration for this paper is the work of 2014 Fields Medalist Artur Avila, and his work in these areas is given special attention.
27 pages. To appear in the Bulletin of the AMS