Title: Dynamical Systems from an Arithmetical Viewpoint

Speaker: Joseph Silverman, Brown University Arithmetic dynamics is the study of number theoretic questions that arise when polynomial or rational maps are iterated. Two examples:

  1. If φ(z) is in Q(z) and α is in Q, under what circumstances can the forward orbit {α,φ(α),φ2(α),...} under iteration of φ contain infinitely many integers?
  2. How many α in Q can be periodic, or more generally have a finite orbit, under iteration of φ?
In this talk I will survey some of the known results and some of the major open questions in arithmetic dynamics. As time permits, I will conclude by discussing recent joint work with Shu Kawaguchi on dynamical canonical heights and on nonarchimedean (p-adic) analogs of classical Green functions.