Degenerations of <span class="mathjax-formula">$\protect \mathrm{SL}(2, \protect \mathbb{C})$</span> representations and Lyapunov exponents

Dujardin, Romain; Favre, Charles

doi:10.5802/ahl.24

Dujardin, Romain; Favre, Charles

Degenerations of

SL (2, ℂ)

representations and Lyapunov exponents

Annales Henri Lebesgue, Volume 2 (2019) , pp. 515-565.

Metadata

DOI10.5802/ahl.24

Abstract

We study the asymptotic behavior of the Lyapunov exponent in a meromorphic family of random products of matrices in $SL (2, ℂ)$ , as the parameter converges to a pole. We show that the blow-up of the Lyapunov exponent is governed by a quantity which can be interpreted as the non-Archimedean Lyapunov exponent of the family. We also describe the limit of the corresponding family of stationary measures on $ℙ^{1} (ℂ)$ .

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