What are Lyapunov exponents, and why are they interesting?
Dynamical Systems
2016-08-10 v1 Mathematical Physics
Geometric Topology
math.MP
Spectral Theory
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, Teichm\"uller theory, and the spectral theory of one-frequency Schr\"odinger 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.
Keywords
Cite
@article{arxiv.1608.02843,
title = {What are Lyapunov exponents, and why are they interesting?},
author = {Amie Wilkinson},
journal= {arXiv preprint arXiv:1608.02843},
year = {2016}
}
Comments
27 pages. To appear in the Bulletin of the AMS