4 papers
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 inj…
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
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.