Renormalization and Siegel disks for complex H\'enon maps

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.