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arXiv · 2605.02459

Random dynamics of plane polynomial automorphisms

Arnaud Nerrière
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Abstract

Let $\mu$ be a finitely supported probability measure on the group of automorphisms of $\mathbb{A}^2_\mathbb{C}$. If the group generated by the support of $\mu$ is non-elementary and contains only loxodromic elements, we show the existence of dynamical Green functions associated to random products. We derive consequences for $\mu$-stationary measures: they are compactly supported, and we can apply Roda's theorem to show stiffness when the action is non-dissipative.

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Arnaud Nerrière. 2026-05-04. Random dynamics of plane polynomial automorphisms. https://arxiv.org/abs/2605.02459

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