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Pré-Publication, Document De Travail Année : 2023

Structure of hyperbolic polynomial automorphisms of C^2 with disconnected Julia sets

Résumé

For a hyperbolic polynomial automorphism of C^2 with a disconnected Julia set, and under a mild dissipativity condition, we give a topological description of the components of the Julia set. Namely, there are finitely many "quasi-solenoids" that govern the asymptotic behavior of the orbits of all non-trivial components. This can be viewed as a refined Spectral Decomposition for a hyperbolic map, as well as a two-dimensional version of the (generalized) Branner-Hubbard theory in one-dimensional polynomial dynamics. An important geometric ingredient of the theory is a John-like property of the Julia set in the unstable leaves.
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Dates et versions

hal-04224944 , version 1 (02-10-2023)

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Romain Dujardin, Mikhail Lyubich. Structure of hyperbolic polynomial automorphisms of C^2 with disconnected Julia sets. 2023. ⟨hal-04224944⟩
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