6 papers · 1 filter
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…
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.
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…
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…
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…