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Dynamical Systems on Homogeneous Spaces
 
Alexander N. Starkov Moscow State University, Moscow, Russia
Front Cover for Dynamical Systems on Homogeneous Spaces
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Hardcover ISBN: 978-0-8218-1389-8
Product Code: MMONO/190
List Price: $122.00
MAA Member Price: $109.80
AMS Member Price: $97.60
Electronic ISBN: 978-1-4704-4604-8
Product Code: MMONO/190.E
List Price: $115.00
MAA Member Price: $103.50
AMS Member Price: $92.00
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
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Dynamical Systems on Homogeneous Spaces
Alexander N. Starkov Moscow State University, Moscow, Russia
Available Formats:
Hardcover ISBN:  978-0-8218-1389-8
Product Code:  MMONO/190
List Price: $122.00
MAA Member Price: $109.80
AMS Member Price: $97.60
Electronic ISBN:  978-1-4704-4604-8
Product Code:  MMONO/190.E
List Price: $115.00
MAA Member Price: $103.50
AMS Member Price: $92.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $183.00
MAA Member Price: $164.70
AMS Member Price: $146.40
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 1902000; 243 pp
    MSC: Primary 37; Secondary 11; 22;

    A homogeneous flow is a dynamical system generated by the action of a closed subgroup \(H\) of a Lie group \(G\) on a homogeneous space of \(G\). The study of such systems is of great significance because they constitute an algebraic model for more general and more complicated systems. Also, there are abundant applications to other fields of mathematics, most notably to number theory.

    The present book gives an extensive survey of the subject. In the first chapter the author discusses ergodicity and mixing of homogeneous flows. The second chapter is focused on unipotent flows, for which substantial progress has been made during the last 10–15 years. The culmination of this progress was M. Ratner's celebrated proof of far-reaching conjectures of Raghunathan and Dani. The third chapter is devoted to the dynamics of nonunipotent flows. The final chapter discusses applications of homogeneous flows to number theory, mainly to the theory of Diophantine approximations. In particular, the author describes in detail the famous proof of the Oppenheim-Davenport conjecture using ergodic properties of homogeneous flows.

    Readership

    Graduate students and research mathematicians working in dynamical systems and ergodic theory.

  • Table of Contents
     
     
    • Chapters
    • Preliminaries
    • Ergodicity and mixing of homogeneous flows
    • Dynamics of unipotent flows
    • Dynamics of nonunipotent flows
    • Applications to number theory
  • Additional Material
     
     
  • Reviews
     
     
    • The book would be very useful to experts as well as those who wish to learn the topic. While experts would benefit from the breadth of the coverage and find it a convenient reference, the learners would relish many proofs that are more palatable compared to the original sources.

      Mathematical Reviews
    • This book provides a thorough discussion of many of the main topics in the field. Theorems are stated precisely, references are provided when proofs are omitted and the historical development of the subject id described, so the book is a very useful reference.

      Bulletin of the LMS
  • Request Review Copy
  • Get Permissions
Volume: 1902000; 243 pp
MSC: Primary 37; Secondary 11; 22;

A homogeneous flow is a dynamical system generated by the action of a closed subgroup \(H\) of a Lie group \(G\) on a homogeneous space of \(G\). The study of such systems is of great significance because they constitute an algebraic model for more general and more complicated systems. Also, there are abundant applications to other fields of mathematics, most notably to number theory.

The present book gives an extensive survey of the subject. In the first chapter the author discusses ergodicity and mixing of homogeneous flows. The second chapter is focused on unipotent flows, for which substantial progress has been made during the last 10–15 years. The culmination of this progress was M. Ratner's celebrated proof of far-reaching conjectures of Raghunathan and Dani. The third chapter is devoted to the dynamics of nonunipotent flows. The final chapter discusses applications of homogeneous flows to number theory, mainly to the theory of Diophantine approximations. In particular, the author describes in detail the famous proof of the Oppenheim-Davenport conjecture using ergodic properties of homogeneous flows.

Readership

Graduate students and research mathematicians working in dynamical systems and ergodic theory.

  • Chapters
  • Preliminaries
  • Ergodicity and mixing of homogeneous flows
  • Dynamics of unipotent flows
  • Dynamics of nonunipotent flows
  • Applications to number theory
  • The book would be very useful to experts as well as those who wish to learn the topic. While experts would benefit from the breadth of the coverage and find it a convenient reference, the learners would relish many proofs that are more palatable compared to the original sources.

    Mathematical Reviews
  • This book provides a thorough discussion of many of the main topics in the field. Theorems are stated precisely, references are provided when proofs are omitted and the historical development of the subject id described, so the book is a very useful reference.

    Bulletin of the LMS
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