论文标题
非理性无动物吸引子的维度悖论
Dimension paradox of irrationally indifferent attractors
论文作者
论文摘要
在本文中，我们以非理性无关的固定点研究了霍明态图的吸引子的几何形状。我们证明，对于一组这样的全体形态系统，固定点的局部吸引子具有Hausdorff尺寸的第二，前提是在固定点处的渐近旋转是足够高的类型，并且不属于Herman数字。作为即时推论，任何此类理性图的Julia集的Hausdorff尺寸都等于两个。此外，我们表明，对于一类渐近旋转数字，吸引子可以满足Karpińska的维度悖论。也就是说，吸引子的终点的集合具有尺寸二，但是如果没有这些终点，则尺寸下降到一个。
In this paper we study the geometry of the attractors of holomorphic maps with an irrationally indifferent fixed point. We prove that for an open set of such holomorphic systems, the local attractor at the fixed point has Hausdorff dimension two, provided the asymptotic rotation at the fixed point is of sufficiently high type and does not belong to Herman numbers. As an immediate corollary, the Hausdorff dimension of the Julia set of any such rational map with a Cremer fixed point is equal to two. Moreover, we show that for a class of asymptotic rotation numbers, the attractor satisfies Karpińska's dimension paradox. That is, the the set of end points of the attractor has dimension two, but without those end points, the dimension drops to one.
