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 …

Abstract Motivated by Lang–Vojta's conjecture, we show that the set of dominant rational self-
maps of an algebraic variety over a number field with only finitely many rational points in any …

Let K be a number field, let φ ∈ K (t) be a rational map of degree at least 2, and let α, β ∈ K.
We show that if α is not in the forward orbit of β, then there is a positive proportion of primes …

Let X/C be a smooth projective variety, let f: X→ X be a dominant rational map, and let f∗: NS
(X) R→ NS (X) R be the induced map on the Néron–Severi group NS (X) R= NS (X)⊗ R …

We study the orbits of a polynomial f∈ C [X], namely, the sets {α, f (α), f (f (α)),…} with α∈ C.
We prove that if two nonlinear complex polynomials f, g have orbits with infinite intersection …

Let $ f $ be a dominant endomorphism of a smooth projective surface $ X $ over an
algebraically closed field $\mathbf {k} $ of characteristic $0 $. We prove that if there is no …

We prove several rigidity results on multiplier and length spectrum. For example, we show
that for every non-exceptional rational map $ f:\mathbb {P}^ 1 (\mathbb {C})\to\mathbb {P}^ 1 …

Given a polynomial f (z)= zd+ c∈ K [z] over a global field K and a 0∈ K, we study the density
of prime ideals of K dividing at least one element of the orbit of a 0 under f. We show that for …

arXiv:1503.00773v2 [math.AG] 5 Nov 2015 Page 1 THE DYNAMICAL MORDELL-LANG
CONJECTURE FOR POLYNOMIAL ENDOMORPHISMS OF THE AFFINE PLANE JUNYI XIE …

There are three aims of this note. The first one is to report some advances around the
dynamical Mordell-Lang (= DML) conjecture. Second, we generalize some known results …