Structural instability of semi-Siegel Hénon maps

Abstract

We show that the dynamics of sufficiently dissipative semi-Siegel complex Hénon maps with golden-mean rotation number is not J-stable in a very strong sense. By the work of Dujardin and Lyubich, this implies that the Newhouse phenomenon occurs for a dense Gδ set of parameters in this family. Another consequence is that the Julia sets of such maps are disconnected for a dense set of parameters.