A formula with some applications to the theory of Lyapunov exponents
Dynamical Systems
2009-12-18 v2 Rings and Algebras
Abstract
We prove an elementary formula about the average expansion of certain products of 2 by 2 matrices. This permits us to quickly re-obtain an inequality by M. Herman and a theorem by Dedieu and Shub, both concerning Lyapunov exponents. Indeed, we show that equality holds in Herman's result. Finally, we give a result about the growth of the spectral radius of products.
Cite
@article{arxiv.math/0104103,
title = {A formula with some applications to the theory of Lyapunov exponents},
author = {Artur Avila and Jairo Bochi},
journal= {arXiv preprint arXiv:math/0104103},
year = {2009}
}
Comments
11 pages, no figures, final version, accepted by the Israel Journal of Mathematics