Title :

Non-recurrence sets for weakly mixing linear dynamical systems

Author(s) :

Grivaux, Sophie [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Ergodic Theory and Dynamical Systems

Pages :

132-152

Publisher :

Cambridge University Press (CUP)

Publication date :

2014

ISSN :

0143-3857

English keyword(s) :

Recurrence and non-recurrence sets
weakly mixing dynamical systems
linear dynamical systems
Jamison sequences
Gaussian measures.

HAL domain(s) :

Mathématiques [math]/Systèmes dynamiques [math.DS]

English abstract : [en]

We study non-recurrence sets for weakly mixing dynamical systems by using linear dynamical systems. These are systems consisting of a bounded linear operator acting on a separable complex Banach space X, which becomes a ...
Show more >We study non-recurrence sets for weakly mixing dynamical systems by using linear dynamical systems. These are systems consisting of a bounded linear operator acting on a separable complex Banach space X, which becomes a probability space when endowed with a non-degenerate Gaussian measure. We generalize some recent results of Bergelson, del Junco, Lemańczyk and Rosenblatt, and show in particular that sets {n k } such that n_{k+1}/ n_k → +∞, or such that n_k divides n_{k+1} for each k ≥ 0, are non-recurrence sets for weakly mixing linear dynamical systems. We also give examples, for each r ≥ 1, of r-Bohr sets which are non-recurrence sets for some weakly mixing systems.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL