English

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 JJ-stable in a very strong sense. By the work of Dujardin and Lyubich, this implies that the Newhouse phenomenon occurs for a dense GδG_\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.

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}
}
R2 v1 2026-06-23T10:50:12.170Z