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Continuity of Lyapunov exponents for polynomial automorphisms of $\mathbb{C}^2$

Romain Dujardin
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Abstract

We prove two continuity theorems for the Lyapunov exponents of the maximal entropy measure of polynomial automorphisms of $\mathbb{C}^2$. The first continuity result holds for any family of polynomial automorphisms of constant dynamical degree. The second result is the continuity of the upper exponent for families degenerating to a 1-dimensional map.

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Romain Dujardin. 2006-08-23. Continuity of Lyapunov exponents for polynomial automorphisms of $\mathbb{C}^2$. https://arxiv.org/abs/math/0608583

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