Degenerations of SL(2,C) representations and Lyapunov exponents

Romain Dujardin (1) , Charles Favre (2)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
2 CMLS - Centre de Mathématiques Laurent Schwartz

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).

Domaines: Systèmes dynamiques [math.DS]; Topologie géométrique [math.GT]

Romain Dujardin, Charles Favre. Degenerations of SL(2,C) representations and Lyapunov exponents. Annales Henri Lebesgue, 2019, ⟨10.5802/ahl.24⟩. ⟨hal-01736453⟩