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arXiv · 1908.06465

Structural Instability of Semi-Siegel H\'enon maps

Michael Yampolsky·Jonguk Yang
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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.

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Michael Yampolsky, Jonguk Yang. 2019-08-18. Structural Instability of Semi-Siegel H\'enon maps. https://arxiv.org/abs/1908.06465

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