Typical Dynamics of Volume Preserving Homeomorphisms - Couverture rigide

Alpern, Steve; Prasad, V. S.

 
9780521582872: Typical Dynamics of Volume Preserving Homeomorphisms
Couverture rigide
ISBN 10 : 0521582873 ISBN 13 : 9780521582872
Editeur : Cambridge University Press, 2001

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Revue de presse

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 für Mathematik

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Cambridge University Press
Date d'édition
2001
Langue
anglais
ISBN 10 
0521582873
ISBN 13 
9780521582872
Reliure
Relié
Nombre de pages
240
Coordonnées du fabricant
non disponible
Personne responsable
Avery
https://www.avery.fr/

chemin des peupliers 27
Dardilly
France

Autres éditions populaires du même titre

9780521172431: Typical Dynamics of Volume Preserving Homeomorphisms

Edition présentée

ISBN 10 :  0521172438 ISBN 13 :  9780521172431
Editeur : Cambridge University Press, 2011
Couverture souple