The golden-mean semi-Siegel Hénon family is not weakly J*-stable at any parameter, yielding Newhouse phenomenon and disconnected Julia sets on dense parameter sets.
A closing lemma for polynomial automorphisms of C^2
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abstract
We prove that for a polynomial diffeomorphism of C^2 , the support of any invariant measure, apart from a few obvious cases, is contained in the closure of the set of saddle periodic points.
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Structural Instability of Semi-Siegel H\'enon maps
The golden-mean semi-Siegel Hénon family is not weakly J*-stable at any parameter, yielding Newhouse phenomenon and disconnected Julia sets on dense parameter sets.