Searcharxiv⌕ Search

arXiv subjects

Luxian Yang

Publications and source records attributed to Luxian Yang.

5 recordsLinked to original sources
arXiv2026

Rigidity of McMullen Julia sets

We provide a complete quasisymmetric classification of the Julia sets of postcritically finite McMullen maps $f_\lambda(z)=z^n+\lambda/z^n$ with $\lambda\in\mathbb{C}^*$ and $n\geq 2$, and prove that the quasisymmetry group of each such Julia set is exactly the finite dihedral group generated by the natural symmetries of the map. These results establish quasisymmetric rigidity for all topological classes in this family, including Sierpi\'{n}ski-like carpets, necklaces, and clusters, and provide the first known examples of rigid Julia sets in each of the three classes.

math.DS↗
arXiv2025

Non-recurrent rational maps with disconnected Julia set

We prove that every wandering exposed Julia component of a rational map is to a singleton, provided that each wandering Julia component containing critical points is non-recurrent. Moreover, we show that the Julia set contains only finitely many periodic complex-type components if each wandering Julia component containing critical values is non-recurrent.

math.DS↗
arXiv2024

Decomposition of rational maps by stable multicurves

A completely stable multicurve of a post-critically finite rational map induces a combinatorial decomposition. The projections of the small Julia sets are immersed within the original Julia set. We prove that two small Julia sets are disjoint if and only if they are separated by a coiling curve. Furthermore, we prove that a post-critically finite rational map with a coiling curve is renormalizable. Using a similar argument, we give a sufficient condition for a Fatou domain to qualify as a Jordan domain. By tuning polynomails in such a Fatou domain, we provide examples of post-critically finite rational maps with coiling curves.

math.DS↗
arXiv2020

On rational maps with buried critical points

In this paper, we construct geometrically finite rational maps with buried critical points on the boundaries of some hyperbolic components by using the pinching and plumbing deformations.

math.DS↗