A new proof of the Herman-Avila-Bochi formula for Lyapunov exponents of SL(2,R)-cocycles
Alexandre T. Baraviera, Joao Lopes Dias, Pedro Duarte
TL;DR
This paper provides a new, simplified proof of the Herman-Avila-Bochi formula, which calculates the average Lyapunov exponent for certain SL(2,R)-cocycles, using geometric analysis of SL(2,R) actions.
Contribution
It introduces a novel geometric approach to prove the Herman-Avila-Bochi formula, simplifying the understanding of Lyapunov exponents in SL(2,R)-cocycles.
Findings
New geometric proof of the Herman-Avila-Bochi formula
Simplification of the proof process for Lyapunov exponents
Enhanced understanding of SL(2,R) actions on the projective line
Abstract
We study the geometry of the action of SL(2,R) on the projective line in order to present a new and simpler proof of the Herman-Avila-Bochi formula. This formula gives the average Lyapunov exponent of a class of 1-families of SL(2,R)-cocycles.
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