  We provide a computer-assisted proof of one of the central open questions in
one-dimensional renormalization theory -- universality of the golden-mean
Siegel disks. We further show that for every function in the stable manifold of
the golden-mean renormalization fixed point the boundary of the Siegel disk is
a quasicircle which coincides with the closure of the critical orbit, and that
the dynamics on the boundary of the Siegel disk is rigid.
  Furthermore, we extend the renormalization from one-dimensional analytic maps
with a golden-mean Siegel disk to two-dimensional dissipative H\'enon-like maps
and show that the renormalization hyperbolicity result still holds in this
setting.
