Some new examples of recurrence and non-recurrence sets for products of rotations on the unit circle

Title:

Some new examples of recurrence and non-recurrence sets for products of rotations on the unit circle

Creator:

Grivaux, Sophie and Roginskaya, Maria

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7c888163-e6c2-4f85-a336-39eb3ed0ed0e
uuid:7c888163-e6c2-4f85-a336-39eb3ed0ed0e

Subject:

recurrence for dynamical systems, non-recurrence for dynamical systems, rotations of the unit circle, syndetic set, Bohr topology on $\mathbb {Z}$, Bohr set, and $r$-Bohr set

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We study recurrence and non-recurrence sets for dynamical systems on compact spaces, in particular for products of rotations on the unit circle $\mathbb T$. A set of integers is called $r$-Bohr if it is recurrent for all products of $r$ rotations on $\mathbb T$, and Bohr if it is recurrent for all products of rotations on $\mathbb T$. It is a result due to Katznelson that for each $r\ge 1$ there exist sets of integers which are $r$-Bohr but not $(r+1)$-Bohr. We present new examples of $r$-Bohr sets which are not Bohr, thanks to a construction which is both flexible and completely explicit. Our results are related to an old combinatorial problem of Veech concerning syndetic sets and the Bohr topology on $\mathbb Z$, and its reformulation in terms of recurrence sets which is due to Glasner and Weiss.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

603-627

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:3

Harvested from:

CDK

Metadata only:

false