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Elements of Topological Dynamics : MATHEMATICS AND ITS APPLICATIONS (KLUWER ) - J. de Vries

Elements of Topological Dynamics

MATHEMATICS AND ITS APPLICATIONS (KLUWER )

Hardcover

Published: 30th June 1993
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This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa­ is in the tradition of the books [GH] and [EW. The title tions. So this book (,Elements . . . ' rather than 'Introduction . . . ') does not mean that this book should be compared, either in scope or in (intended) impact, with the 'Ele­ ments' of Euclid or Bourbaki. Instead, it reflects the choice and organisation of the material in this book: elementary and basic (but sufficient to understand recent research papers in this field). There are still many challenging prob­ lems waiting for a solution, and especially among general topologists there is a growing interest in this direction. However, the technical inaccessability of many research papers makes it almost impossible for an outsider to under­ stand what is going on. To a large extent, this inaccessability is caused by the lack of a good and systematic exposition of the fundamental methods and techniques of abstract TO. This book is an attempt to fill this gap. The guiding principle for the organization of the material in this book has been the exposition of methods and techniques rather than a discussion of the leading problems and their solutions. though the latter are certainly not neglected: they are used as a motivation wherever possible.

Preface
Notation
Various aspects of the theory of dynamical systemsp. 1
Dynamical systemsp. 1
Ergodic theoryp. 16
Differentiable dynamicsp. 22
Continuous and discrete flowsp. 49
Basic notions for continuous and discrete flowsp. 49
Limit sets and recurrencep. 55
Minimal sets and almost periodic pointsp. 66
Transitive behaviour of open setsp. 73
Continuous vs. discrete flowsp. 85
Invariant measuresp. 94
Morphisms of flowsp. 99
The construction of topologically ergodic, weakly mixing and minimal skew extensionsp. 108
Important examplesp. 151
Flows on circles and torip. 151
Shift systemsp. 162
Function spacesp. 203
The horocycle flow and the geodesic flowp. 212
The general frameworkp. 269
Topological dynamics in the framework of T-spacesp. 269
Equicontinuous, distal and proximal flowsp. 278
Ellis semigroups and the universal enveloping semigroupp. 299
Pointed flows, ambits, and universal ambitsp. 323
Subalgebras of RUC* (T) and ambitsp. 343
Equicontinuity and distalityp. 396
The equicontinuous structure relationp. 396
Distal and equicontinuous extensionsp. 409
The Furstenberg structure theoremp. 427
Ellis groups and algebraic characterization of distal extensionsp. 445
The circle operation, [tau]-topologies, and equicontinuous extensionsp. 463
Structure of extensionsp. 514
Construction of the G-diagramp. 514
RIC-extensionsp. 529
The AG-diagram and the improved G-diagramp. 539
The Veech structure theoremp. 550
Universal extensionsp. 577
Appendix A: Topologyp. 627
Appendix B: Compact right semitopological semigroupsp. 641
Appendix C: Integrationp. 650
Appendix D: Enveloping semigroups and compactificationsp. 662
Appendix E: Topological transformation groupsp. 668
Referencesp. 691
Index of Authorsp. 720
Index of Symbolsp. 726
Index of Termsp. 729
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792322870
ISBN-10: 0792322878
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 748
Published: 30th June 1993
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 17.15  x 3.18
Weight (kg): 1.2