A formula with some applications to the theory of Lyapunov exponents

Artur Avila; Jairo Bochi

doi:10.1007/BF02785853

A formula with some applications to the theory of Lyapunov exponents

Artur Avila, Jairo Bochi

Mathematics

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

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.

Original language	English (US)
Pages (from-to)	125-137
Number of pages	13
Journal	Israel Journal of Mathematics
Volume	131
DOIs	https://doi.org/10.1007/BF02785853
State	Published - 2002

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/BF02785853

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title = "A formula with some applications to the theory of Lyapunov exponents",

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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AU - Bochi, Jairo

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AB - 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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JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

A formula with some applications to the theory of Lyapunov exponents

Abstract

All Science Journal Classification (ASJC) codes

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