ROBOTICS & AUTOMATION
Empowering Progress
Up to 25% off Essentials Robotics and Automation titles
Minimal Flows and Their Extensions
- 1st Edition, Volume 153 - July 1, 1988
- Author: J. Auslander
- Language: English
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 8 7 2 6 4 - 3
This monograph presents developments in the abstract theory of topological dynamics, concentrating on the internal structure of minimal flows (actions of groups on compact… Read more
Purchase options
Institutional subscription on ScienceDirect
Request a sales quoteThis 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.
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.
- No. of pages: 264
- Language: English
- Edition: 1
- Volume: 153
- Published: July 1, 1988
- Imprint: North Holland
- eBook ISBN: 9780080872643
Read Minimal Flows and Their Extensions on ScienceDirect