We study algebraic dynamical systems (and, more generally, σ-varieties) Φ:A^n_C→A^n_C
given by coordinatewise univariate polynomials by refining an old theorem of Ritt on …

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 …

In this paper, we study arithmetic dynamics in arbitrary characteristic, in particular in positive
characteristic. Applying the arithmetic degree and canonical height in positive characteristic …

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 $ X $ be a variety defined over a number field and $ f $ be a dominant rational self-map
of $ X $ of infinite order. We show that $ X $ admits many algebraic points which are not …

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 a special case of a dynamical analogue of the classical Mordell–Lang conjecture.
Specifically, let φ be a rational function with no periodic critical points other than those that …

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 …

The existence of Zariski dense orbits for polynomial endomorphisms of the affine plane Page 1
The existence of Zariski dense orbits for polynomial endomorphisms of the affine plane Junyi …

Ritt studied the functional decomposition of a univariate complex polynomial f into prime
(indecomposable) polynomials, f= u_1 o u_2 o... o u_r. His main achievement was a …