Auslander, Joseph Minimal flows and their extensions. (English) Zbl 0654.54027 North-Holland Mathematics Studies, 153; Notas de Matemática, 122. Amsterdam etc.: North-Holland. xi, 265 p. $ 86.75; Dfl. 165.00 (1988). This book on topological dynamics treats many of the same topics as the monograph by R. Ellis [“Lectures in topological dynamics” (1969; Zbl 0193.515)]. It keeps, however, a more dynamical viewpoint; the algebric aspects are dealt with in a separate chapter. Certainly, the theory of equicontinuous and distal minimal flows (culminatig in Furstenberg’s structure theorem) are central in the field, and so they are presented together with proximality in great detail. One of the main emphasis of the book is put on the universal approach towards minimal flows. So the reader will find the theorems on the existence of universal minimal flows, the existence of “maximal” equicontinuous factors, disjointness, weakly mixing flows among many others. The existence of invariant measures is treated via strongly proximal flows [compare S. Glasner, “Proximal flows”, Lect. Notes Math. 517 (1976; Zbl 0322.54017)]. The book also contains Kakutani-Bebutov theorems on the representation as a flow on function spaces and a final chapter is devoted to general structure theorems, includig PI flows, for example. This well written book fills in a gap presenting recent developments in the theory. Reviewer: M.Denker Cited in 5 ReviewsCited in 289 Documents MSC: 54H20 Topological dynamics (MSC2010) 54-02 Research exposition (monographs, survey articles) pertaining to general topology 28D15 General groups of measure-preserving transformations Keywords:equicontinuous and distal minimal flows; Furstenberg’s structure theorem; universal approach towards minimal flows; equicontinuous factors; disjointness; weakly mixing flows; invariant measures; proximal flows; PI flows Citations:Zbl 0193.515; Zbl 0322.54017 PDFBibTeX XMLCite \textit{J. Auslander}, Minimal flows and their extensions. Amsterdam etc.: North-Holland (1988; Zbl 0654.54027)