A formula with some applications to the theory of Lyapunov exponents |
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Authors: | Artur Avila Jairo Bochi |
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Affiliation: | (1) Collège de France, 3 rue d’Ulm, 75005 Paris, France;(2) IMPA, Estr. D. Castorina 110, 22460-320 Rio de Janeiro, Brazil |
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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. Financial support from Pronex-Dynamical Systems, CNPq 001/2000 and from Faperj is gratefully acknowledged. |
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