The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang
conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point …

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 …

We study definably amenable NIP groups. We develop a theory of generics showing that
various definitions considered previously coincide, and we study invariant measures. As …

We study the postcritically finite maps within the moduli space of complex polynomial
dynamical systems. We characterize rational curves in the moduli space containing an …

We prove the equivalence of dynamical stability, preperiodicity, and canonical height 0, for
algebraic families of rational maps ft: ℙ 1 (ℂ)→ ℙ 1 (ℂ), parameterized by t in a …

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 …

arXiv:2311.16369v1 [math.AG] 27 Nov 2023 Page 1 arXiv:2311.16369v1 [math.AG] 27 Nov
2023 ADVANCES IN THE EQUIVARIANT MINIMAL MODEL PROGRAM AND THEIR …

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 …