Convergence of multiple ergodic averages

Research paper by Bernard Host

Indexed on: 15 Jun '06Published on: 15 Jun '06Published in: Mathematics - Dynamical Systems


These notes are based on a course for a general audience given at the Centro de Modeliamento Matem\'atico of the University of Chile, in December 2004. We study the mean convergence of multiple ergodic averages, that is, averages of a product of functions taken at different times. We also describe the relations between this area of ergodic theory and some classical and some recent results in additive number theory.