Combining ideas of Ihara-Serre-Tate, Lang [5] proved the following natural result. If a (complex, irreducible) plane curve C ⊂ A contains infinitely many points with both coordinates roots of unity, then C is the zero locus of an equation of the form xy = ζ, where a, b ∈ Z and ζ is a root of unity. In other words, if F ∈ C[x, y] is an irreducible polynomial for which there exist infinitely many...

Let φ(z) ∈ Q(z) be a rational function of degree d ≥ 2 with φ(0) = 0 and such that φ does not vanish to order d at 0. Let α ∈ Q have infinite orbit under iteration of φ and write φ(α) = An/Bn as a fraction in lowest terms. We prove that for all but finitely many n ≥ 0, the numerator An has a primitive divisor, i.e., there is a prime p such that p | An and p ∤ Ai for all i < n. More generally, w...

This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a “dynamical” sense. This means precisely that they (semi-) conjugate a given continuous (or measure-preserving) dynamical system and a symbolic one. The classes of dynamical systems and their codings c...

A method of graphical analysis which accounts for cause/effect lag between biological populations and environmental factors is presented. The method involves analysis of ellipsoid curves generated by delayed population responses to cyclic environmental variables. Six ellipse types are distinguished which determine the type of relationship involved and provide a key to equations for calculating ...

This document lists a wide variety of articles and books in the area of arithmetic dynamics. It also includes some additional material that was referenced in The Arithmetic of Dynamical Systems (Springer-Verlag GTM 241) and some miscellaneous articles and books that I’ve referenced in my own work. Note that the numbering in this document does not match the numbering of references in GTM 241. Fu...