广场谢尔皮耶斯基地毯和Lattès地图
Square Sierpiński carpets and Lattès maps
摘要：
证明了标准正方形Sierpienski地毯$S_p$（$p\ge 3$奇）的每一个拟对称同胚都是等距的.这加强和完成了作者的早期工作。我们还表明，一个类似的结论持有的双重$S_p$的外周边圆的拟对称。最后，作为本文方法的一个应用，我们证明了没有标准的正方形地毯$S_p$与后临界有限有理映射的朱利亚集是拟对称等价的.
英文摘要：
We prove that every quasisymmetric homeomorphism of a standard square Sierpiński carpet $S_p$, $p\ge 3$ odd, is an isometry. This strengthens and completes earlier work by the authors. We also show that a similar conclusion holds for quasisymmetries of the double of $S_p$ across the outer peripheral circle. Finally, as an application of the techniques developed in this paper, we prove that no standard square carpet $S_p$ is quasisymmetrically equivalent to the Julia set of a postcritically-finite rational map.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
