Structural Instability of Semi-Siegel H\'enon maps
Dynamical Systems
2019-09-10 v2
Abstract
We show that the dynamics of sufficiently dissipative semi-Siegel complex H\'enon maps with golden-mean rotation number is not -stable in a very strong sense. By the work of Dujardin and Lyubich, this implies that the Newhouse phenomenon occurs for a dense set of parameters in this family. Another consequence is that the Julia sets of such maps are disconnected for a dense set of parameters.
Keywords
Cite
@article{arxiv.1908.06465,
title = {Structural Instability of Semi-Siegel H\'enon maps},
author = {Michael Yampolsky and Jonguk Yang},
journal= {arXiv preprint arXiv:1908.06465},
year = {2019}
}