6 citations · 12 across the 15 of their papers we have counts for
16 papers
Exceptional maps and abelian points in backward orbits
Zhuchao Ji, Jiarui Song, Junyi Xie
Consider a number field , a polarized endomorphism on a normal projective variety, and a non-exceptional point for . We show that the extension $K(f^{-\infty}(…
Genus and Gonality of Small Curves, Dynamical Uniform Boundedness, and Bifurcation
Zhuchao Ji, Junyi Xie
We prove the Gonality Conjecture in arithmetic dynamics: for any non-isotrivial one-parameter algebraic family of rational maps on , the gonality of dist…
Rigidity of Lyapunov exponents for polynomials
Zhuchao Ji, Junyi Xie, Geng-Rui Zhang
Let be polynomials of degree with disconnected Julia sets. We prove that they have the same Lyapunov exponent $\mathcal{L}_f=\mathcal{L}_g…
Equidistribution speed of iterated preimages for rational maps on the Riemann sphere
Mai Hao, Zhuchao Ji
The exponential equidistribution speed of iterated preimages for holomorphic endomorphisms on was established by Drasin-Okuyama for , and by Dinh-Sibony for arb…
A geometric approach to the uniform boundedness of -primary torsion points
Zhuchao Ji, Jiarui Song, Junyi Xie
We prove that for a non-isotrivial abelian scheme over a smooth curve, the genus of a generic sequence of multi-sections with small heights tends to infinity. As an application, we…
Cyclotomic integral points for affine dynamics
Zhuchao Ji, Junyi Xie, Geng-Rui Zhang
Let be a regular endomorphism of algebraic degree (i.e., extends to an endomorphism on of algebraic degree ) defined…
The moduli space of a rational map is Carathéodory hyperbolic
Zhuchao Ji, Junyi Xie
Let be a rational map of degree . The moduli space , introduced by McMullen and Sullivan, is a complex analytic space consisting all quasiconformal conj…
The multiplier spectrum morphism is generically injective
Zhuchao Ji, Junyi Xie
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…
Space spanned by characteristic exponents
Zhuchao Ji, Junyi Xie, Geng-Rui Zhang
We prove several rigidity results on multiplier spectrum and length spectrum. For example, we show that for every non-exceptional rational map $f:\mathbb{P}^1(\mathbb{C})\to\mathbb…
DAO for curves
Zhuchao Ji, Junyi Xie
We prove the Dynamical André-Oort (DAO) conjecture proposed by Baker and DeMarco for families of rational maps parameterized by an algebraic curve. In fact, we prove a stronger res…
Local rigidity of Julia sets
Zhuchao Ji, Junyi Xie
We find criteria ensuring that a local (holomorphic, real analytic, ) homeomorphism between the Julia sets of two given rational functions comes from an algebraic corresponden…
The wandering domain problem for attracting polynomial skew products
Zhuchao Ji, Weixiao Shen
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…
Homoclinic orbits, multiplier spectrum and rigidity theorems in complex dynamics
Zhuchao Ji, Junyi Xie
The aims of this paper are to answer several conjectures and questions about multiplier spectrum of rational maps and to give new proofs of several rigidity theorems in complex dyn…
Structure of Julia sets for post-critically finite endomorphisms on
Zhuchao Ji
Let be a post-critically finite endomorphism (PCF map for short) on , let denote the Julia set and let denote the support of the measure of maximal en…
Non-uniform hyperbolicity in polynomial skew products
Zhuchao Ji
Let be a polynomial skew product which leaves invariant an attracting vertical line . Assume moreover restricted to is non-uniformly h…
Non-wandering Fatou components for strongly attracting polynomial skew products
Zhuchao Ji
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 po…