Renormalization and Siegel disks for complex H\'enon maps
Dynamical Systems
2019-12-24 v6
Abstract
We use hyperbolicity of golden-mean renormalization of dissipative H\'enon-like maps to prove that the boundaries of Siegel disks of sufficiently dissipative quadratic complex H\'enon maps with golden-mean rotation number are topological circles. Conditionally on an appropriate renormalization hyperbolicity property, we derive the same result for Siegel disks of H\'enon maps with all eventually periodic rotation numbers.
Keywords
Cite
@article{arxiv.1604.07069,
title = {Renormalization and Siegel disks for complex H\'enon maps},
author = {Denis Gaidashev and Remus Radu and Michael Yampolsky},
journal= {arXiv preprint arXiv:1604.07069},
year = {2019}
}
Comments
arXiv admin note: text overlap with arXiv:1604.00717