刺猬的正面积和不可达不动点
Positive area and inaccessible fixed points for hedgehogs
摘要：
设f是在C中原点具有无理性中立不动点的全纯双同态芽（即f（0）= 0，f '（0）= e2 pi i alpha，alpha in R-Q）.佩雷斯-马可表明存在一个独特的家庭的非平凡不变的充分连续包含不动点称为Siegel rectata。当f是非线性的（即不全纯共轭的刚性旋转R_{alpha}（z）= e 2 pi i z）的不变紧被称为刺猬。佩雷斯-马可开发的技术建设的例子，非线性化的芽;这些被用来建设的作者对冲猪的豪斯多夫维数之一，并适应Cheritat建设西格尔磁盘与伪圆边界。我们利用这些技巧构造了正面积的刺猬和具有不可达不动点的刺猬。
英文摘要：
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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