Some rigidity results for polynomial automorphisms of C^2
Résumé
We prove several new rigidity results for automorphisms of 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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