Sets of k-recurrence but not (k+1)-recurrence

Details Sets of k-recurrence but not (k+1)-recurrence Sets of k-recurrence but not (k+1)-recurrence

2005-03-17

arxiv.org/abs/math/0503367v2

Mathematics

Dynamical Systems

8 pages

Scientific paper

For every $k\in \mathbb{N}$, we produce a set of integers which is
$k$-recurrent but not $(k+1)$-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.

Affiliated with

Also associated with

No associations

Rating

Sets of k-recurrence but not (k+1)-recurrence does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sets of k-recurrence but not (k+1)-recurrence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sets of k-recurrence but not (k+1)-recurrence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-606248