Abstract. Let D be a bounded domain in C 2 with a non-compact group of holomorphic automorphisms. Model domains for D are obtained under the hypotheses that at least one orbit accumulates at a boundary point near which the boundary is smooth, real analytic and of finite type.
Abstract. We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains. It is shown that such mappings extend smoothly up to the closures of the domains, provided each factor of the source satisfies Condition R. It also shown that the number of smoothly bounded factors in the source and target must be the same, and the proper holomorphic map splits as product of proper mappings between the factor domains.
The purpose of this note is to explore further the rigidity properties of Hénon maps from [5]. For instance, we show that if H and F are Hénon maps with the same Green measure (µH = µF ), or the same filled Julia set (KH = KF ), or the same Green function (GH = GF ), then H 2 and F 2 have to commute. This in turn, gives that H and F have the same non-escaping sets. Further we prove that, either of the association of a Hénon map H to its Green measure µH or to its filled Julia set KH or to its Green function GH is locally injective.
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