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

S. Grivaux ; Maria Roginskaya (Institutionen för matematiska vetenskaper, matematik)
Czechoslovak Mathematical Journal (0011-4642). Vol. 63 (2013), 3, p. 603-627.
[Artikel, refereegranskad vetenskaplig]

We study recurrence and non-recurrence sets for dynamical systems on compact spaces, in particular for products of rotations on the unit circle T. A set of integers is called r-Bohr if it is recurrent for all products of r rotations on T, and Bohr if it is recurrent for all products of rotations on T. It is a result due to Katznelson that for each r a (c) 3/4 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 a"currency sign, and its reformulation in terms of recurrence sets which is due to Glasner and Weiss.

Nyckelord: recurrence for dynamical systems, non-recurrence for dynamical systems, rotations of the unit circle, syndetic set, Bohr topology on Z, Bohr, set, r-Bohr set, graphs



Denna post skapades 2013-12-17. Senast ändrad 2014-09-29.
CPL Pubid: 189491

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur