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Let g be a polynomial automorphism of C2. In a similar way as is done for polynomials inC, we denote byK± the set of points inC2 with bounded forward/ backward orbit under g. We writeJ ± = ∂K± andJ = J+ ∩ J−. We refer toJ ± as the positive/negative Julia set and to J as the Julia set of g. The setJ ± is unbounded, closed, and connected, while J is compact (see [BS2; BS3; FM; HO] for more details). The purpose of the main part of this paper is to show that, under the assumption thatg is a hyperbolic mapping (i.e., the Julia set J is a hyperbolic set for g), the complete information about the Hausdorff dimensions of J+ andJ− is already contained in the Julia set J itself. In particular, the results of Theorem 4.1–4.4 can be summarized by the following result.

Dimension of Julia sets of polynomial automorphisms of C2.