Data di Pubblicazione:
2023
Citazione:
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.
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Algebra in the Stone-Cech compactification; Dynamical system; F-uniform recurrence; F-proximality; JIFUR;
Elenco autori:
L. Luperi Baglini, S. Kanti Patra, M. Moid Shaikh
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