Typical Dynamics of Volume Preserving Homeomorphisms

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.

First Sentence

Two of the principal analytic structures that may be put on a set X are measure and topology.

Subjects

Other Editions

• Typical Dynamics of Volume Preserving HomeomorphismsHardcoverCambridge University Press2001-03-15
• Typical Dynamics of Volume Preserving HomeomorphismsCambridge University Press2000-01-01
• Typical Dynamics of Volume Preserving HomeomorphismsCambridge University Press2001-01-01
• Typical Dynamics of Volume Preserving HomeomorphismsCambridge University Press2001-01-01
• Typical Dynamics of Volume Preserving HomeomorphismsCambridge University Press2005-01-01
• Typical Dynamics of Volume Preserving HomeomorphismsCambridge University Press2009-01-01