Random dynamics of plane polynomial automorphisms
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917457869930496 |
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| author | Nerrière, Arnaud |
| author_facet | Nerrière, Arnaud |
| contents | Let $μ$ 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 $μ$ is non-elementary and contains only loxodromic elements, we show the existence of dynamical Green functions associated to random products. We derive consequences for $μ$-stationary measures: they are compactly supported, and we can apply Roda's theorem to show stiffness when the action is non-dissipative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02459 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Random dynamics of plane polynomial automorphisms Nerrière, Arnaud Dynamical Systems Algebraic Geometry Complex Variables Let $μ$ 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 $μ$ is non-elementary and contains only loxodromic elements, we show the existence of dynamical Green functions associated to random products. We derive consequences for $μ$-stationary measures: they are compactly supported, and we can apply Roda's theorem to show stiffness when the action is non-dissipative. |
| title | Random dynamics of plane polynomial automorphisms |
| topic | Dynamical Systems Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2605.02459 |