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arXiv:math/0104103 [math.DS]AbstractReferencesReviewsResources

A formula with some applications to the theory of Lyapunov exponents

Artur Avila, Jairo Bochi

Published 2001-04-09, updated 2001-11-06Version 2

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.

Comments: 11 pages, no figures, final version, accepted by the Israel Journal of Mathematics
Journal: Israel Journal of Mathematics, 131 (2002), 125-137.
Categories: math.DS, math.RA
Subjects: 34D08, 15A04
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