Recurrence along generalized polynomials
by
Inger Knutson
University of Agder, Norway

A generalized polynomial is a real-valued function which is obtained from the conventional polynomials by use of the operations of addition, multiplication, and taking the greatest integer part. Generalized polynomials show up naturally in ergodic theory. In particular, there are strong relations between bounded generalized polynomials and translations on nilmanifolds (recently established by Bergelson and Leibman). We will survey some results concerning uniform distribution of generalized polynomials, and discuss questions related to recurrence along generalized polynomial sequences.

Date received: February 25, 2008