Smooth Combs Inside Hedgehogs

Mathematics – Dynamical Systems

Scientific paper

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Scientific paper

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-H\"older regular.

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