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Structural Instability of Semi-Siegel Hénon maps (1908.06465v2)
Published 18 Aug 2019 in math.DS
Abstract: We show that the dynamics of sufficiently dissipative semi-Siegel complex H\'enon 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 $G_\delta$ set of parameters in this family. Another consequence is that the Julia sets of such maps are disconnected for a dense set of parameters.