Minimal flows and their extensions
Author(s)
Bibliographic Information
Minimal flows and their extensions
(North-Holland mathematics studies, 153)(Notas de matemática, 122)
North-Holland , Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1988
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC19:514/Au722070091307
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Description and Table of Contents
Description
This monograph presents developments in the abstract theory of topological dynamics, concentrating on the internal structure of minimal flows (actions of groups on compact Hausdorff spaces for which every orbit is dense) and their homomorphisms (continuous equivariant maps).Various classes of minimal flows (equicontinuous, distal, point distal) are intensively studied, and a general structure theorem is obtained. Another theme is the ``universal'' approach - entire classes of minimal flows are studied, rather than flows in isolation. This leads to the consideration of disjointness of flows, which is a kind of independence condition. Among the topics unique to this book are a proof of the Ellis ``joint continuity theorem'', a characterization of the equicontinuous structure relation, and the aforementioned structure theorem for minimal flows.
Table of Contents
Flows and Minimal Sets. Equicontinuous Flows. The Enveloping Semigroup of a Transformation Group, I. Joint Continuity Theorems. Distal Flows. The Enveloping Semigroup, II. The Furstenberg Structure Theorem for Distal Minimal Flows. Universal Minimal Flows and Ambits. The Equicontinuous Structure Relation and Weakly Mixing Flows. The Algebraic Theory of Minimal Flows. Disjointness. Invariant Measures on Flows. Kakutani-Bebutov Theorems. General Structure Theorems. Appendices: Nets. Uniform Spaces.
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