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Israel Journal of Mathematics

, Volume 131, Issue 1, pp 125–137 | Cite as

A formula with some applications to the theory of Lyapunov exponents

  • Artur Avila
  • Jairo Bochi
Article

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

Lyapunov Exponent Random Matrice Spectral Radius Elementary Formula Positive Exponent 
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References

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Copyright information

© The Hebrew University Magnes Press 2002

Authors and Affiliations

  1. 1.Collège de FranceParisFrance
  2. 2.IMPARio de JaneiroBrazil

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