University of Georgia
Mathematics Department Colloquium
Michael Zieve
University of Southern California
February 11, 1999
Algebraic dynamical systems
Abstract: Quite generally, a (discrete) dynamical system is a mapping
from a set to itself; one studies the behavior of points of the set
upon repeated application of the mapping. Classically the set has
been taken to be the Riemann sphere, and the mapping to be a rational
function or power series. In recent years there has been much work on
algebraic dynamical systems, where the mapping respects some algebraic
structure on the set. I will discuss some results and explain their
connection to arithmetic geometry, complex dynamics, theoretical
physics, and pseudorandom number generation.