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October  2005, 12(5): 853-880. doi: 10.3934/dcds.2005.12.853

Smooth combs inside hedgehogs

Kingshook Biswas 1,

1. 

Department of Mathematics, University of California, Los Angeles, CA 90095, United States

Received  October 2003 Revised  November 2004 Published  February 2005

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.
Keywords: combs., hedgehogs, Irrational indifferent fixed points.
Mathematics Subject Classification: Primary 37F50, 30D0.
Citation: Kingshook Biswas. Smooth combs inside hedgehogs. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 853-880. doi: 10.3934/dcds.2005.12.853
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