Structure of hyperbolic polynomial automorphisms of C² with disconnected Julia sets

For a hyperbolic polynomial automorphism of (Formula presented.) 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 nontrivial 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.