Complexity of Nilsystems and systems lacking nilfactors - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue Journal d'analyse mathématique Année : 2014

Complexity of Nilsystems and systems lacking nilfactors

Résumé

Nilsystems are a natural generalization of rotations and arise in various contexts, including in the study of multiple ergodic averages in ergodic theory, in the structural analysis of topological dynamical systems, and in asymptotics for patterns in certain subsets of the integers. We show, however, that many natural classes in both measure preserving systems and topological dynamical systems contain no higher order nilsystems as factors, meaning that the only nilsystems they contain as factors are rotations. Our main result is that in the topological setting, nilsystems have a particular type of complexity of polynomial growth, where the polynomial (with explicit degree) is an asymptotic both from below and above. We also deduce several ergodic and topological applications of these results.

Dates et versions

hal-01252512 , version 1 (07-01-2016)

Identifiants

Citer

Bernard Host, Bryna Kra, Alejandro Maass. Complexity of Nilsystems and systems lacking nilfactors. Journal d'analyse mathématique, 2014, 124, pp.261-295. ⟨10.1007/s11854-014-0032-7⟩. ⟨hal-01252512⟩
46 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More