Israel Journal of Mathematics

, Volume 131, Issue 1, pp 125–137

A formula with some applications to the theory of Lyapunov exponents


DOI: 10.1007/BF02785853

Cite this article as:
Avila, A. & Bochi, J. Isr. J. Math. (2002) 131: 125. doi: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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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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