Typical Dynamics of Volume Preserving Homeomorphisms
Published on 17. February 2011
Book
Paperback/Softback
238 pages
978-0-521-17243-1 (ISBN)
Description
This 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley-Zehnder- Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property.
Reviews / Votes
Review of the hardback: 'An interesting piece of research for the specialist.' Mathematika Review of the hardback: 'The authors of this book are undoubtedly the experts of generic properties of measure preserving homeomorphisms of compact and locally compact manifolds, continuing and extending ground-breaking early work by J. C. Oxtoby and S. M. Ulam. The book is very well and carefully written and is an invaluable reference for anybody working on the interface between topological dymanics and ergodic theory.' Monatshefte fuer MathematikMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 14 mm
Weight
393 gr
ISBN-13
978-0-521-17243-1 (9780521172431)
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Schweitzer Classification
Other editions
Additional editions
Steve Alpern | V. S. Prasad
Typical Dynamics of Volume Preserving Homeomorphisms
E-Book
01/2005
1st Edition
Cambridge University Press
€27.99
Available for download
Steve Alpern | V. S. Prasad
Typical Dynamics of Volume Preserving Homeomorphisms
Book
03/2001
Cambridge University Press
€145.70
Shipment within 15-20 days
Persons
Content
Historical Preface; General outline; Part I. Volume Preserving Homomorphisms of the Cube: 1. Introduction to Parts I and II (compact manifolds); 2. Measure preserving homeomorphisms; 3. Discrete approximations; 4. Transitive homeomorphisms of In and Rn; 5. Fixed points and area preservation; 6. Measure preserving Lusin theorem; 7. Ergodic homeomorphisms; 8. Uniform approximation in G[In, ?] and generic properties in ?[In, ?]; Part II. Measure Preserving Homeomorphisms of a Compact Manifold: 9. Measures on compact manifolds; 10. Dynamics on compact manifolds; Part III. Measure Preserving Homeomorphisms of a Noncompact Manifold: 11. Introduction to Part III; 12. Ergodic volume preserving homeomorphisms of Rn; 13. Manifolds where ergodic is not generic; 14. Noncompact manifolds and ends; 15. Ergodic homeomorphisms: the results; 16. Ergodic homeomorphisms: proof; 17. Other properties typical in M[X, ?]; Appendix 1. Multiple Rokhlin towers and conjugacy approximation; Appendix 2. Homeomorphic measures; Bibliography; Index.