6 papers · 1 filter
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 .
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…
On the dynamical Mordell-Lang conjecture in positive characteristic
Junyi Xie, She Yang
We solve the dynamical Mordell-Lang conjecture for bounded-degree dynamical systems in positive characteristic. The answer in this case disproves the original version of the pDML c…
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…