Typical Dynamics of Volume Preserving Homeomorphisms

Steve Alpern

ISBN 10: 0521582873 / ISBN 13: 9780521582872

Published by Cambridge University Press, 2001

About this Item

Druck auf Anfrage Neuware - Printed after ordering - This book provides a self-contained introduction to typical properties of volume preserving homeomorphisms, examples of which include transitivity, chaos and ergodicity. The authors make the first part of the book very concrete by focusing on volume preserving homeomorphisms of the unit n-dimensional cube. They also prove fixed point theorems (Conley-Zehnder-Franks). This is done in a number of short self-contained chapters that would be suitable for an undergraduate analysis seminar or a graduate lecture course. Parts Two and Three consider compact manifolds and sigma compact manifolds respectively, describing the work of the two authors in extending the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property.

Seller Inventory # 9780521582872

Bibliographic Details

• Title: Typical Dynamics of Volume Preserving Homeomorphisms
• Publisher: Cambridge University Press
• Publication Date: 2001
• Language: English
• ISBN 10: 0521582873
• ISBN 13: 9780521582872
• Binding: Buch
• Condition: Neu
• Dimensions: 235W x 157H x 19D millimeters 235 millimeters width by 157 millimeters height by 19 millimeters depth
• Weight: 546 grams

About this title

Synopsis

This book provides a self-contained introduction to typical properties of volume preserving homeomorphisms, examples of which include transitivity, chaos and ergodicity. The authors make the first part of the book very concrete by focusing on volume preserving homeomorphisms of the unit n-dimensional cube. They also prove fixed point theorems (Conley-Zehnder-Franks). This is done in a number of short self-contained chapters that would be suitable for an undergraduate analysis seminar or a graduate lecture course. Parts Two and Three consider compact manifolds and sigma compact manifolds respectively, describing the work of the two authors in extending the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property.

Book Description

This book provides a self-contained introduction to typical properties of volume preserving homeomorphisms. Stress is given to the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. Part I focuses on volume preserving homeomorphisms of the unit n-dimensional cube. Parts II and III consider compact manifolds and sigma compact manifolds respectively, describing the work of the authors in extending the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property.