Sets of k-recurrence but not (k+1)-recurrence
Dynamical Systems
2007-05-23 v2 Combinatorics
Abstract
For every , we produce a set of integers which is -recurrent but not -recurrent. This extends a result of Furstenberg who produced a 1-recurrent set which is not 2-recurrent. We discuss a similar result for convergence of multiple ergodic averages. Finally, we also point out a combinatorial consequence related to Szemer\' edi's theorem.
Cite
@article{arxiv.math/0503367,
title = {Sets of k-recurrence but not (k+1)-recurrence},
author = {N. Frantzikinakis and E. Lesigne and M. Wierdl},
journal= {arXiv preprint arXiv:math/0503367},
year = {2007}
}
Comments
8 pages