عنوان

Dynamical systems of algebraic origin /

(Number (ISBN

3034802773

(Number (ISBN

3034892365

(Number (ISBN

9783034802772

(Number (ISBN

9783034892360

Erroneous ISBN

0817651748

Erroneous ISBN

3764351748

Erroneous ISBN

9780817651749

Erroneous ISBN

9783034899574

Erroneous ISBN

9783764351748

Title Proper

Dynamical systems of algebraic origin /

General Material Designation

[Book]

First Statement of Responsibility

Klaus Schmidt.

Place of Publication, Distribution, etc.

Boston :

Name of Publisher, Distributor, etc.

Birkhäuser Verlag,

Date of Publication, Distribution, etc.

[1995]

Date of Publication, Distribution, etc.

©1995

Specific Material Designation and Extent of Item

1 online resource (xviii, 310 pages) :

Other Physical Details

illustrations

Series Title

Progress in mathematics ;

Volume Designation

v. 128

Text of Note

Includes bibliographical references (pages 301-305) and index.

Text of Note

Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing aclass of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups. One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting from this connection allows the construction of examples with a variety of specified dynamical properties, and by combining algebraic and dynamical tools one obtains a quite detailed understanding of this class of Zd-actions. ----------------------- It is a marvelous display of the richness and depth of the interplay between dynamical systems on one hand and commutative algebra and number theory on the other. (...) This book is a very valuable addition to the literature on dynamical systems and ergodic theory. (Mathematical Reviews) This beautifully written monograph (...) is a very important addition to the literature, giving the first systematic account of the ergodic theory of algebraic Zd-actions. It will be of immense value to any researchers and graduate students interested in such multi-dimensional actions. (Zentralblatt MATH).

Text of Note

Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.

Title

Dynamical systems of algebraic origin.

Abelian groups.

Automorphisms.

Differentiable dynamical systems.

Ergodic theory.

Abelian groups.

Algebraische Geometrie

Automorphismes.

Automorphisms.

Differentiable dynamical systems.

Dynamique différentiable.

Dynamisches System

Ergodic theory.

Groupes abéliens.

Kommutative Algebra

Kompakte Gruppe

Théorie ergodique.

Number

Edition

Class number

Book number

Class number

System Code

Schmidt, Klaus,1943-

Date of Transaction

20200823094741.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y