A formula with some applications to the theory of Lyapunov exponents

Artur Avila, Jairo Bochi

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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.

Original languageEnglish (US)
Pages (from-to)125-137
Number of pages13
JournalIsrael Journal of Mathematics
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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