A motivation for the paper [BS1] was the earlier work by Ruelle and Sullivan
[RS]. Ruelle and Sullivan consider diffeomorphisms which
are *Axiom A* (which means that they are hyperbolic on the nonwandering set, and the periodic points
are dense in the nonwandering set). A hyperbolic map has laminations by stable manifolds and unstable manifolds.
Ruelle and Sullivan show that for Axiom A diffeomorphisms, the stable and unstable manifolds can be given the
structure of *geometric currents*. This is done by using the theory of Axiom A maps.

On the other hand, a complex Hénon map has the function *G*^{+}, and so there is always
a current *dd*^{c}G^{+}. In [BS1] it is shown that if *J* is a hyperbolic set for
*f*, then *f* is Axiom A. In addition, the currents *dd*^{c}G^{+} and
*dd*^{c}G^{-} have the structure of geometric currents as given in [RS].

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