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.
The purpose of this paper is to present several examples of non-autonomous basins of attraction that arise from sequences of automorphisms of C k . In the first part, we prove that the non-autonomous basin of attraction arising from a pair of automorphisms of C 2 of a prescribed form is biholomorphic to C 2 . This, in particular, provides a partial answer to a question raised in [2] in connection with Bedford's Conjecture about uniformizing stable manifolds. In the second part, we describe three examples of Short C k 's with specified properties. First, we show that for k ≥ 3, there exist (k − 1) mutually disjoint Short C k 's in C k . Second, we construct a Short C k , large enough to accommodate a Fatou-Bieberbach domain, that avoids a given algebraic variety of codimension 2. Lastly, we discuss examples of Short C k 's with (piece-wise) smooth boundaries.
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