论文标题
含有“ y”的准自用相似的分形大于一个尺寸
Quasi-self-similar fractals containing "Y" have dimension larger than one
论文作者
论文摘要
假设$ x $是一个紧凑的连接度量空间，$ f：x \ to x $是Haïssinsky-Pilgrim的意义上的度量粗糙的相结合图。我们表明，如果$ x $包含字母“ y”的同构副本，那么$ x $的hausdorff尺寸大于一个。作为一个应用程序，我们表明，对于半Hyperbolic有理地图$ f $ f $它的Julia Set $ \ Mathcal {J} _f $是准对称的，等于具有Hausdorff Dimension 1的空间，并且仅当$ \ Mathcal {j} {j} _f $是同源的，而不是$ \ nathcal {j} _f $是同源的。
Suppose $X$ is a compact connected metric space and $f: X \to X$ is a metric coarse expanding conformal map in the sense of Haïssinsky-Pilgrim. We show that if $X$ contains a homeomorphic copy of the letter "Y", then the Hausdorff dimension of $X$ is greater than one. As an application, we show that for a semi-hyperbolic rational map $f$ its Julia set $\mathcal{J}_f$ is quasi-symmetric equivalent to a space having Hausdorff dimension 1 if and only if $\mathcal{J}_f$ is homeomorphic to a circle or a closed interval.
