The boundaries of golden-mean Siegel disks in the complex quadratic   H\'enon family are not smooth
  As was recently shown by the first author and others, golden-mean Siegel disks of sufficiently dissipative complex quadratic H\'enon maps are bounded by topological circles. In this paper we investigate the geometric properties of such curves, and demonstrate that they cannot be $C^1$-smooth. 
Michael Yampolsky, Jonguk Yang
math.DS