Alpern, S. and Prasad, V. (2001) Typical dynamics of volume preserving homeomorphisms. Cambridge Tracts in Mathematics, 139 . Cambridge, UK: Cambridge University Press. ISBN 9780511543180

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Abstract

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.

Item Type:	Book
Divisions:	Faculty of Social Sciences > Warwick Business School > Operational Research & Management Sciences Faculty of Social Sciences > Warwick Business School
Series Name:	Cambridge Tracts in Mathematics
Publisher:	Cambridge University Press
Place of Publication:	Cambridge, UK
ISBN:	9780511543180
Editor:	Alpern, S. and Prasad, V.
Official Date:	2001
Dates:	Date Event 2001 Published
Volume:	139
Status:	Peer Reviewed
Publication Status:	Published
Related URLs:	Other

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