论文标题
朱莉娅（Julia）的豪斯多夫（Hausdorff）
Hausdorff dimension of Julia sets in the logistic family
论文作者
论文摘要
封闭的间隔和圆圈是多项式动力学中唯一平滑的朱莉娅集。 D. ruelle证明，朱莉娅单一朱莉娅的豪斯多夫尺寸靠近圆圈取决于参数。在Mandelbrot集M的尖端附近，Hausdorff尺寸通常是不连续的。回答J-C的问题。 Yoccoz在共形设置中，我们观察到，二次朱莉娅集的Hausdorff维度不断取决于$ c $，并在M尖端找到了M端的显式界限，从1维lebesgue Measure的意义上讲，对于大多数真实参数。
A closed interval and circle are the only smooth Julia sets in polynomial dynamics. D. Ruelle proved that the Hausdorff dimension of unicritical Julia sets close to the circle depends analytically on the parameter. Near the tip of the Mandelbrot set M, the Hausdorff dimension is generally discontinuous. Answering a question of J-C. Yoccoz in the conformal setting, we observe that the Hausdorff dimension of quadratic Julia sets depends continuously on $c$ and find explicit bounds at the tip of M for most real parameters in the the sense of 1-dimensional Lebesgue measure.
