4 papers · 1 filter
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…
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…
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.
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…