Zobrazeno 1 - 10
of 25
pro vyhledávání: '"Ji, Zhuchao"'
Autor:
Ji, Zhuchao, Xie, Junyi
Let $f$ be a rational map of degree $d\geq 2$. The moduli space $\mathcal{M}_f$, introduced by McMullen and Sullivan, is a complex analytic space consisting all quasiconformal conjugacy classes of $f$. For $f$ that is not flexible Latt\`es, we show t
Externí odkaz:
http://arxiv.org/abs/2404.04568
Autor:
Ji, Zhuchao, Xie, Junyi
In this paper, we consider the multiplier spectrum of periodic points, which is a natural morphism defined on the moduli space of rational maps on the projective line. A celebrated theorem of McMullen asserts that aside from the well-understood flexi
Externí odkaz:
http://arxiv.org/abs/2309.15382
We prove several rigidity results on multiplier and length spectrum. For example, we show that for every non-exceptional rational map $f:\mathbb{P}^1(\mathbb{C})\to\mathbb{P}^1(\mathbb{C})$ of degree $d\geq2$, the $\mathbb{Q}$-vector space generated
Externí odkaz:
http://arxiv.org/abs/2308.00289
Autor:
Ji, Zhuchao, Xie, Junyi
We prove the Dynamical Andr\'e-Oort (DAO) conjecture proposed by Baker and DeMarco for families of rational maps parameterized by an algebraic curve. In fact, we prove a stronger result, which is a Bogomolov type generalization of DAO for curves.
Externí odkaz:
http://arxiv.org/abs/2302.02583
Autor:
Ji, Zhuchao, Xie, Junyi
We find criteria ensuring that a local (holomorphic, real analytic, $C^1$) homeomorphism between the Julia sets of two given rational functions comes from an algebraic correspondence. For example, we show that if there is a local $C^1$-symmetry betwe
Externí odkaz:
http://arxiv.org/abs/2302.02562
Autor:
Ji, Zhuchao, Shen, Weixiao
Wandering Fatou components were recently constructed by Astorg et al for higher dimensional holomorphic maps on projective spaces. Their examples are polynomial skew products with a parabolic invariant line. In this paper we study this wandering doma
Externí odkaz:
http://arxiv.org/abs/2209.01715
Autor:
Ji, Zhuchao, Xie, Junyi
The aims of this paper are answering several conjectures and questions about multiplier spectrum of rational maps and giving new proofs of several rigidity theorems in complex dynamics, by combining tools from complex and non-archimedean dynamics. A
Externí odkaz:
http://arxiv.org/abs/2205.13258
Autor:
Ji, Zhuchao
Publikováno v:
Mathematische Annalen, 2021
Let $f$ be a post-critically finite endomorphism (PCF map for short) on $\mathbb{P}^2$, let $J_1$ denote the Julia set and let $J_2$ denote the support of the measure of maximal entropy. In this paper we show that: 1. $J_1\setminus J_2$ is contained
Externí odkaz:
http://arxiv.org/abs/2010.11094
Autor:
Ji, Zhuchao
Publikováno v:
International Mathematics Research Notices, 2022
Let $f:\mathbb{C}^2\to \mathbb{C}^2$ be a polynomial skew product which leaves invariant an attracting vertical line $ L $. Assume moreover $f$ restricted to $L$ is non-uniformly hyperbolic, in the sense that $f$ restricted to $L$ satisfies one of th
Externí odkaz:
http://arxiv.org/abs/1909.06084
Autor:
Ji, Zhuchao
Publikováno v:
The Journal of Geometric Analysis, 2020
We show a partial generalization of Sullivan's non-wandering domain theorem in complex dimension two. More precisely, we show the non-existence of wandering Fatou components for polynomial skew products of $ \mathbb{C}^2$ with an invariant attracting
Externí odkaz:
http://arxiv.org/abs/1802.05972