Structural Instability of Semi-Siegel H\'enon maps
- Resource Type
- Working Paper
- Authors
- Yampolsky, Michael; Yang, Jonguk
- Source
- Subject
- Mathematics - Dynamical Systems
- Language
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.