García-Ferreira, S.; Sanchis, M. Ultrafilter-limit points in metric dynamical systems. (English) Zbl 1199.54194 Commentat. Math. Univ. Carol. 48, No. 3, 465-485 (2007). If \(X\) is a compact space, \(f\) a continuous self-map of \(X\) and \(p\) a free ultrafilter on the set of natural numbers, the authors define \(f^p\) to be the pointwise limit of the iterates \(f^n\), \(n=1,2,\dots \), along the ultrafilter \(p\). The paper contains characterizations of continuity of \(f^p\) (at a point or on the whole space \(X\)), some results on the relationship of \(f^p\) and \(f^q\) for two distinct ultrafilters \(p,q\), a study of particular properties of \(f^p\) for a \(P\)-point \(p\) and some results relating this kind of limits to actions on metrizable semigroups. Reviewer: Ondřej Kalenda (Praha) Cited in 12 Documents MSC: 54H20 Topological dynamics (MSC2010) 54D80 Special constructions of topological spaces (spaces of ultrafilters, etc.) Keywords:ultrafilter; \(P\)-point; dynamical system; limit along an ultrafilter PDFBibTeX XMLCite \textit{S. García-Ferreira} and \textit{M. Sanchis}, Commentat. Math. Univ. Carol. 48, No. 3, 465--485 (2007; Zbl 1199.54194) Full Text: EuDML EMIS