论文标题
关于多项式的Hausdorff维
On Hausdorff dimension of polynomial not totally disconnected Julia sets
论文作者
论文摘要
我们证明，对于一个至少2个复合度变量的多项式，朱莉娅集合没有完全断开，也没有一个圆，也没有间隔，此朱莉娅集的hausdorff尺寸大于1。到现在为止，这仅在连接的朱莉娅集合案例中才知道。我们还提供了一个多项式的示例，该示例具有非连接但不是完全断开连接的朱莉娅集合，因此，其所有组成的组成部分都超过单个点是分析性的，因此克里斯托弗·毕晓普（Christopher Bishop）解决了一个问题，他们询问每个组件是否必须使hausdorff dimension dimension大于1。
We prove that for every polynomial of one complex variable of degree at least 2 and Julia set not being totally disconnected nor a circle, nor interval, Hausdorff dimension of this Julia set is larger than 1. Till now this was known only in the connected Julia set case. We give also an example of a polynomial with non-connected but not totally disconnected Julia set and such that all its components comprising of more than single points are analytic arcs, thus resolving a question by Christopher Bishop, who asked whether every such component must have Hausdorff dimension larger than 1.
