Smooth combs inside hedgehogs

Kingshook Biswas

doi:10.3934/dcds.2005.12.853

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2005, Volume 12, Issue 5: 853-880. Doi: 10.3934/dcds.2005.12.853

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Smooth combs inside hedgehogs

Kingshook Biswas^1,

1.
Department of Mathematics, University of California, Los Angeles, CA 90095

Received: September 30, 2003

Revised: October 31, 2004

Published: September 2005

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Abstract

We use techniques of tube-log Riemann surfaces due to R.Pérez-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.

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Mathematics Subject Classification: Primary 37F50, 30D05.

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