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math.DS2026
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…
math.DS2025
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…
math.DS2023
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…