2024/11/15 by Serge Cantat, Romain Dujardin, Cantat, Serge +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Quantum chaos and dynamical systems #Mathematical Dynamics and Fractals
paper · pdf · doi:10.4310/cjm.260722225236
We prove several new rigidity results for polynomial automorphisms of C2 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. The properties of multipliers of saddle periodic orbits play an important role in these results. We also study some arithmetic questions related to these multipliers.