A formula with some applications to the theory of Lyapunov exponents

Details A formula with some applications to the theory of Lyapunov exponents A formula with some applications to the theory of Lyapunov exponents

2001-04-09

arxiv.org/abs/math/0104103v2

Israel Journal of Mathematics, 131 (2002), 125-137.

Mathematics

Dynamical Systems

11 pages, no figures, final version, accepted by the Israel Journal of Mathematics

Scientific paper

10.1007/BF02785853

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.

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