Correspondence and translation principles for the Mandelbrot set

Mandelbrot集中本原分量的Sturmian外角

Sturmian external angles of primitive components in the Mandelbrot set

本研究提出可计算给定期数周期Sturmian角及其Mandelbrot集着陆参数的折线构造法，给出计算其共轭角的简易方法，并证明此类Sturmian角的二进制展开与揉序列一一对应。

Misiurewicz点处Multibrot集与对应关系的Julia集之间的相似性

Similarity between the Multibrot set and the Julia set of correspondences at Misiurewicz points

本研究证明在Misiurewicz点处，代数对应关系的Julia集渐近自相似，且Multibrot集与Julia集渐近相似，并给出横截性条件的代数证明及实验支持。

对应模交配族的离散轨迹的镶嵌

Tessellating the discreteness locus for the modular mating family of correspondences

该研究针对黎曼球上2:2全纯对应模交配族的离散轨迹，构造了双曲平面到其补集的典范解析映射，诱导出镶嵌并提出相关结构猜想，揭示了其与经典曼德博集合的拓扑关联。

二次映射与模群的配对 III：模Mandelbrot集

Mating quadratic maps with the modular group III: The modular Mandelbrot set

本研究证明Bullett-Penrose(2:2)全纯对应族的连通性轨迹与抛物Mandelbrot集间存在动力学同胚，结合已有结论推导出该轨迹与经典Mandelbrot集同胚，完善了二次映射与模群配对的相关理论。

Dynamics of continued fractions and kneading sequences of unimodal maps

In this paper we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, the alpha-continued fraction transformations T_alpha and unimodal maps. This correspondence identifies bifurcation parameters in the two families, and allows one to transfer topological and metric properties from one setting to the other. As an application, we recover results about the real slice of the Mandelbrot set, and the set of univoque numbers.

（反）全纯对应下的共形测度

Conformal measures of (anti)holomorphic correspondences

本文研究（反）全纯对应极限集的共形测度，证明满足临界指数、相对双曲性及极小性条件时极限集存在非原子共形测度且豪斯多夫维数小于2，并将结论推广至Bullett--Penrose对应与LLMM对应。