Hausdorff dimension of Julia sets of complex Henon mappings

The Hausdorff dimension of closed invariant sets under diffeomorphisms is an interesting concept as it is a measure of their complexity. The theory of holomorphic dynamical systems provides us with many examples of fractal sets and, in particular, a theorem of Ruelle [Ru1] shows that the Hausdorff dimension of the Julia set depends real analytically on f if f is a rational function of C and the Julia set J of f is hyperbolic. In this paper we generalize Ruelle's result for complex dimension two and show the real analytic dependence of the Hausdorff dimension of the corresponding Julia sets of hyperbolic Henon mappings.