Holder continuous Siegel disc boundary curves

We prove, with the assistance of rigorous computer calculations, that Widom's renormalization fixed point (1983), and any pair in its domain of attraction, has a Holder continuous invariant curve through the origin. We deduce that any complex analytic map attracted by Widom's fixed point has a Siegel disc bounded by a Holder continuous Jordan curve passing through a critical point of the map. It is known empirically that the stable manifold of Widom's fixed point has real codimension two. This would imply that the above holds on an open set of maps having a golden mean Siegel disc.