In this paper, we establish a theory of adelic line bundles over quasi-projective varieties over
finitely generated fields. Besides definitions of adelic line bundles, we consider their …

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 …

In this article, we combine complex-analytic and arithmetic tools to study the preperiodic
points of 1-dimensional complex dynamical systems. We show that for any fixed a, b∈ C …

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

In this article, we consider a dominant rational self-map $ f: X\dashrightarrow X $ of a normal
projective variety defined over a number field. We study the arithmetic degree $\alpha_k (f) …

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 …

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 …

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 …