We study the localization along a filter of several dynamical notions. This generalizes and extends similar localizations that have been considered in the literature, e.g. near 0 and near an idempotent. Definitions and basic properties of F-syndetic, piecewise F-syndetic, collectionwise F-piecewise syndetic, F-quasi central and F-central sets and their relations with F-uniformly recurrent points and ultrafilters are studied. We provide also the nonstandard characterizations of some of the above notions and we prove the partition regularity of several nonlinear equations along filters under mild general assumptions.
Dynamical notions along filters / L. Luperi Baglini, S. Kanti Patra, M. Moid Shaikh. - In: NEW YORK JOURNAL OF MATHEMATICS. - ISSN 1076-9803. - 29:(2023 Jun 30), pp. 792-817.
Dynamical notions along filters
L. Luperi Baglini
Primo
;
2023
Abstract
We study the localization along a filter of several dynamical notions. This generalizes and extends similar localizations that have been considered in the literature, e.g. near 0 and near an idempotent. Definitions and basic properties of F-syndetic, piecewise F-syndetic, collectionwise F-piecewise syndetic, F-quasi central and F-central sets and their relations with F-uniformly recurrent points and ultrafilters are studied. We provide also the nonstandard characterizations of some of the above notions and we prove the partition regularity of several nonlinear equations along filters under mild general assumptions.File | Dimensione | Formato | |
---|---|---|---|
29-31p(1).pdf
accesso aperto
Tipologia:
Publisher's version/PDF
Dimensione
823.85 kB
Formato
Adobe PDF
|
823.85 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.