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arXiv · 1803.07324

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

Romain Dujardin·Charles Favre
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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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Romain Dujardin, Charles Favre. 2018-03-20. Degenerations of SL(2,C) representations and Lyapunov exponents. https://arxiv.org/abs/1803.07324

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