Smooth Combs Inside Hedgehogs

Abstract

We use techniques of tube-log Riemann surfaces due to R.Perez-Marco to construct a hedgehog containing smooth $C^{\infty }$ combs. The hedgehog is a common hedgehog for a family of commuting non-linearisable holomorphic maps with a common indifferent fixed point. The comb is made up of smooth curves, and is transversally bi-Hölder regular.