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arXiv · 2411.10339

Some rigidity results for polynomial automorphisms of C^2

Serge Cantat·Romain Dujardin
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Abstract

We prove several new rigidity results for polynomial automorphisms of $\mathbb C^2$ with positive entropy. A first result is that a complex slice of the (forward or backward) Julia set is never a smooth, or even rectifiable, curve. We also show that such an automorphism cannot preserve a global holomorphic foliation, nor a real-analytic foliation with complex leaves. These results are used to show that under mild assumptions, two real-analytically conjugate automorphisms are polynomially conjugate. For mappings defined over a number field, we also study the fields of definition of multipliers of saddle periodic orbits.

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Serge Cantat, Romain Dujardin. 2024-11-15. Some rigidity results for polynomial automorphisms of C^2. https://doi.org/10.4310/cjm.260722225236

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