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

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

2006-08-23

arxiv.org/abs/math/0608583v1

Mathematics

Dynamical Systems

Scientific paper

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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