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A formula with some applications to the theory of Lyapunov exponents

Artur Avila·Jairo Bochi
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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.

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Artur Avila, Jairo Bochi. 2001-11-06. A formula with some applications to the theory of Lyapunov exponents. https://doi.org/10.1007/bf02785853

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