Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A
relatively new field, it draws inspiration partly from dynamical analogues of theorems and …

arxiv:2302.02583v2 [math.DS] 27 Sep 2023 Page 1 DAO FOR CURVES ZHUCHAO JI AND
JUNYI XIE Abstract. We prove the Dynamical André-Oort (DAO) conjecture proposed by …

Let be a smooth curve defined over, let and let be an algebraic family of rational maps
indexed by all. We study whether there exist infinitely many such that both and are …

In the moduli space of degree polynomials, special subvarieties are those cut out by critical
orbit relations, and then special points are the post-critically finite polynomials. It was …

We prove that Zhang's dynamical Bogomolov conjecture holds uniformly along $1 $-
parameter families of rational split maps and curves. This provides dynamical analogues of …

We establish equidistribution with respect to the bifurcation measure of postcritically finite
(PCF) maps in any one-dimensional algebraic family of unicritical polynomials. Using this …

Unlikely Intersection for Two-Parameter Families of Polynomials | International Mathematics
Research Notices | Oxford Academic Skip to Main Content Advertisement Oxford Academic …

We will show that the Mandelbrot set is locally conformally inhomogeneous; the only
conformal map defined in an open set intersecting and satisfying is the identity map. The …

We study the dynamics of algebraic families of maps on Pn, over the field C of complex
numbers, and the geometry of their preperiodic points. The goal of this note is to formulate a …

We study the dynamics of algebraic families of maps on $\mathbb {P}^ N $, over the field
$\mathbb {C} $ of complex numbers, and the geometry of their preperiodic points. The goal …