activity
20242026
collaborators

7 papers

math.DS2026

Height arguments toward the dynamical Mordell-Lang problem in arbitrary characteristic

Junyi Xie, She Yang

We use height arguments to prove two results about the dynamical Mordell-Lang problem. (i) For an endomorphism of a projective variety, the return set of a dense orbit into a curve…

math.DS2026

Dynamical Mordell-Lang problem for automorphisms of surfaces in positive characteristic

Junyi Xie, She Yang

We solve the dynamical Mordell-Lang problem in positive characteristic for automorphisms of projective surfaces.

math.DS2026

Dynamical Mordell-Lang conjecture for split self-maps of affine curve times projective curve

Junyi Xie, She Yang, Aoyang Zheng

We prove the dynamical Mordell-Lang conjecture for product of endomorphisms of an affine curve and a projective curve over .

math.AG2025

Rigidity in Complex Dynamics: Multiplier Spectrum and Dynamical André-Oort Conjecture

Junyi Xie

In this note, we present recent progress on rigidity problems in one-dimensional complex dynamics, including the proof of Dynamical André-Oort conjecture for curves and generic in…

math.DS2025

Arithmetic Degrees are Cohomological Lyapunov Multipliers

Jiarui Song, Junyi Xie, She Yang

For endomorphisms of projective varieties, we prove that the arithmetic degree of a point with Zariski dense orbit must be a cohomological Lyapunov multiplier of the dynamical syst…

math.DS2025

Algebraic dynamics and recursive inequalities

Junyi Xie

We get three basic results in algebraic dynamics: (1). We give the first algorithm to compute the dynamical degrees to arbitrary precision. (2). We prove that for a family of domin…