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. - (2022 Apr 04).

Dynamical notions along filters

L. Luperi Baglini
;
2022

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.
Settore MAT/01 - Logica Matematica
https://arxiv.org/abs/2204.01344
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/938917
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