7 papers · 1 filter
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…
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 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…