The Boundaries of Golden-Mean Siegel Disks in the Complex Quadratic Hénon Family Are Not Smooth

Abstract

As was recently shown by the first author and others in Gaidashev et al. (Renormalization and Siegel disks for complex Henon maps, [12]), golden-mean Siegel disks of sufficiently dissipative complex quadratic Hénon maps are bounded by topological circles. In this paper we investigate the geometric properties of such curves, and demonstrate that they cannot be C1-smooth.