论文标题
朱莉娅单位对应关系的豪斯多夫尺寸
Hausdorff dimension of Julia sets of unicritical correspondences
论文作者
论文摘要
我们表明，如果$β> 1 $是一个合理的数字，而Holomorphic对应关系的Julia设置$ J $ $ z^β+c $最终在本地是一个本地上的驱虫剂，那么$ j $的hausdorff尺寸是由相关压力功能的零上述界定的。结果，我们得出的结论是，每当$ q^2 <p $和$β= $β= p/q $以最低的程度时，对应关系的朱莉娅集合的参数量为零。
We show that if $β>1$ is a rational number and the Julia set $J$ of the holomorphic correspondence $z^β+c$ is a locally eventually onto hyperbolic repeller, then the Hausdorff dimension of $J$ is bounded from above by the zero of the associated pressure function. As a consequence, we conclude that the Julia set of the correspondence has zero Lebesgue measure for parameters close to zero, whenever $q^2<p$ and $β=p/q$ in lowest terms.
