English

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.

Keywords

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