Uniform perfectness of the Berkovich Julia sets in non-archimedean dynamics

Non-archimedean connected Julia sets with branching

We construct the first examples of rational functions defined over a non-archimedean field with certain dynamical properties. In particular, we find such functions whose Julia sets, in the Berkovich projective line, are connected but not contained in a line segment. We also show how to compute the measure-theoretic and topological entropy of such maps. In particular, we show for some of our examples that the measure-theoretic entropy is strictly smaller than the topological entropy, thus answering a question of Favre and Rivera-Letelier.

局部域、迭代扩张与朱利亚集

Local fields, iterated extensions, and Julia Sets

研究局部域上迭代扩张的性质，揭示其行为仅依赖于参数c的估值，完成对所有ℓ≥2的分类，并关联分形结构与朱利亚集。

Wandering Fatou Components and Algebraic Julia Sets

We study the dynamics of polynomials with coefficients in a non-Archimedean field $K,$ where $K$ is a field containing a dense subset of algebraic elements over a discrete valued field $k.$ We prove that every wandering Fatou component is contained in the basin of a periodic orbit. We obtain a complete description of the new Julia set points that appear when passing from $K$ to the Berkovich line over $K$. We give a dynamical characterization of polynomials having algebraic Julia sets. More precisely, we establish that a polynomial with algebraic coefficients has algebraic Julia set if every c…

非阿基米德与混合设定下朱利亚集的连续性

Continuity of the Julia sets in non-archimedean and hybrid settings

该研究针对完备非阿基米德域上Berkovich空间及带混合范数的复空间参数化的单变量有理函数族，证明了朱利亚集在豪斯多夫拓扑下连续性的类似Mané--Sad--Sullivan定理结果。

Berkovich 射影线上的斜积

Skew Products on the Berkovich Projective Line

本文在非阿基米德域上的 Berkovich 射影线上引入并系统研究了斜积的动力学理论，涵盖周期点、Fatou/Julia 二分法，并最终分类了 Fatou 集的连通分支。

Repelling periodic points and logarithmic equidistribution in non-archimedean dynamics

It is an open problem whether repelling periodic points are dense in the classical Julia set of a non-archimedean rational function of degree more than one. We give a partial positive answer to this question based on a study of a logarithmic equidistribution on the Berkovich projective line over non-archimedean fields.