Junyi Xie

works on

arithmetic dynamics 1 bifurcation theory 1 dynatomic curves 1 gonality 1 uniform boundedness 1

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math.DS2026

Genus and Gonality of Small Curves, Dynamical Uniform Boundedness, and Bifurcation

Zhuchao Ji, Junyi Xie

The paper proves that the gonality of dynatomic curves in non‑isotrivial families of rational maps on the projective line grows without bound, and uses this to obtain uniform bound…

math.DS2026

Cyclotomic integral points for affine dynamics

Zhuchao Ji, Junyi Xie, Geng-Rui Zhang

Let $f : A^{N} \to A^{N}$ be a regular endomorphism of algebraic degree $d \geq 2$ (i.e., $f$ extends to an endomorphism on $P^{N}$ of algebraic degree $d$ ) defined…

math.DS2025

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…