A formula with some applications to the theory of Lyapunov exponents
classification
🧮 math.DS
math.RA
keywords
exponentsformulahermanlyapunovproductsresultapplicationsaverage
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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.
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