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:
-
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?
-
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.