Structure of hyperbolic polynomial automorphisms of C^2 with disconnected Julia sets
Dynamical Systems
2023-09-26 v1 Complex Variables
Abstract
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.
Keywords
Cite
@article{arxiv.2309.14135,
title = {Structure of hyperbolic polynomial automorphisms of C^2 with disconnected Julia sets},
author = {Romain Dujardin and Mikhail Lyubich},
journal= {arXiv preprint arXiv:2309.14135},
year = {2023}
}