  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.
