Colorado State University  Mathematical

Dynamical Systems from a Number Theorist's Perspective

By  Joseph Silverman
From  Department of Mathematics
Brown University, Providence, RI
When  February 20, 2008
4:00 pm
Where  Weber 223
Abstract  Dynamics is the study of iteration of functions, while number theorists often study integer and rational solutions to equations. The new field of arithmetic dynamics involves number theoretic questions that arise when polynomial or rational maps are iterated. Here are two typical problems:
  1. If f(z) is a rational function with rational coefficients and c is an initial rational number, under what circumstances can the set of iterates {c, f(c), f(f(c)), f(f(f(c))), ...} contain infinitely many integers?
  2. For a given rational function f(z) with rational coefficients, how many initial rational values c have a finite set of iterates?
In this talk I will discuss what is known and what is conjectured about these and other problems in arithmetic dynamics. The talk will require no background in either number theory or dynamics.
Jeff Achter

There will be Refreshments in Weber 117 at 3.30pm
The Colloquium counts as Seminar Credit for Mathematics Students.