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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.

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Book Details

ISBN: 9780521582872
ISBN-10: 0521582873
Format: Hardback
(228mm x 152mm x 17mm)
Pages: 240
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 29-Mar-2001
Country of Publication: United Kingdom

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Books By Author Steve Alpern