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.