Junyi Xie

activity

20242026

collaborators

4 papers

math.DS2026

Rigidity of Lyapunov exponents for polynomials

Zhuchao Ji, Junyi Xie, Geng-Rui Zhang

Let $f, g \in Q [z]$ be polynomials of degree $d \geq 2$ with disconnected Julia sets. We prove that they have the same Lyapunov exponent $\mathcal{L}_f=\mathcal{L}_g…

math.AG2025

Tate's question, Standard conjecture D, semisimplicity and Dynamical degree comparison conjecture

Fei Hu, Tuyen Trung Truong, Junyi Xie

Let $X$ be a smooth projective variety of dimension $n$ over the algebraic closure of a finite field $F_{p}$ . Assuming the standard conjecture $D$ , we prove a weaker form of…

math.DS2025

Numerical action for endomorphisms

Junyi Xie

Let $f : X \to X$ be a surjective endomorphism of a projective variety of dimension $d$ . The aim of this paper is to study the action of $f$ on the numerical group of divisors. For e…

math.AG2024

Arithmetic degree and its application to Zariski dense orbit conjecture

Yohsuke Matsuzawa, Junyi Xie

We prove that for a dominant rational self-map $f$ on a quasi-projective variety defined over $Q$ , there is a point whose $f$ -orbit is well-defined and its arit…