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arXiv · 1010.4496

Positive area and inaccessible fixed points for hedgehogs

Kingshook Biswas
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Abstract

Let f be a germ of holomorphic diffeomorphism with an irra- tionally indifferent fixed point at the origin in C (i.e. f(0) = 0, f'(0) = e 2pi i alpha, alpha in R - Q). Perez-Marco showed the existence of a unique family of nontrivial invariant full continua containing the fixed point called Siegel compacta. When f is non-linearizable (i.e. not holomorphically conjugate to the rigid rotation R_{alpha}(z) = e 2pi i z) the invariant compacts obtained are called hedgehogs. Perez-Marco developed techniques for the construction of examples of non-linearizable germs; these were used by the author to construct hedge- hogs of Hausdorff dimension one, and adapted by Cheritat to construct Siegel disks with pseudo-circle boundaries. We use these techniques to construct hedgehogs of positive area and hedgehogs with inaccessible fixed points.

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Kingshook Biswas. 2010-10-21. Positive area and inaccessible fixed points for hedgehogs. https://doi.org/10.1017/etds.2014.143

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