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Ergodic Theory of Numbers
 
Ergodic Theory of Numbers
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-88385-034-3
Product Code:  CAR/29
List Price: $45.00
MAA Member Price: $33.75
AMS Member Price: $33.75
eBook ISBN:  978-1-61444-027-7
Product Code:  CAR/29.E
List Price: $35.00
MAA Member Price: $26.25
AMS Member Price: $26.25
Hardcover ISBN:  978-0-88385-034-3
eBook: ISBN:  978-1-61444-027-7
Product Code:  CAR/29.B
List Price: $80.00 $62.50
MAA Member Price: $60.00 $46.88
AMS Member Price: $60.00 $46.88
Ergodic Theory of Numbers
Click above image for expanded view
Ergodic Theory of Numbers
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-88385-034-3
Product Code:  CAR/29
List Price: $45.00
MAA Member Price: $33.75
AMS Member Price: $33.75
eBook ISBN:  978-1-61444-027-7
Product Code:  CAR/29.E
List Price: $35.00
MAA Member Price: $26.25
AMS Member Price: $26.25
Hardcover ISBN:  978-0-88385-034-3
eBook ISBN:  978-1-61444-027-7
Product Code:  CAR/29.B
List Price: $80.00 $62.50
MAA Member Price: $60.00 $46.88
AMS Member Price: $60.00 $46.88
  • Book Details
     
     
    The Carus Mathematical Monographs
    Volume: 292002; 190 pp
    MSC: Primary 37; Secondary 11; 28

    Ergodic Theory of Numbers looks at the interaction between two fields of mathematics: number theory and ergodic theory (as part of dynamical systems). It is an introduction to the ergodic theory behind common number expansions, like decimal expansions, continued fractions, and many others. However, its aim does not stop there. For undergraduate students with sufficient background knowledge in real analysis and graduate students interested in the area, it is also an introduction to a "dynamical way of thinking".

    The questions studied here are dynamical as well as number theoretical in nature, and the answers are obtained with the help of ergodic theory. Attention is focused on concepts like measure-preserving, ergodicity, natural extension, induced transformations, and entropy. These concepts are then applied to familiar expansions to obtain old and new results in an elegant and straightforward manner. What it means to be ergodic and the basic ideas behind ergodic theory will be explained along the way. The subjects covered vary from classical to recent, which makes this book appealing to researchers as well as students.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Introduction
    • Chapter 2. Variations on a theme (Other expansions)
    • Chapter 3. Ergodicity
    • Chapter 4. Systems obtained from other systems
    • Chapter 5. Diophantine approximation and continued fractions
    • Chapter 6. Entropy
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 292002; 190 pp
MSC: Primary 37; Secondary 11; 28

Ergodic Theory of Numbers looks at the interaction between two fields of mathematics: number theory and ergodic theory (as part of dynamical systems). It is an introduction to the ergodic theory behind common number expansions, like decimal expansions, continued fractions, and many others. However, its aim does not stop there. For undergraduate students with sufficient background knowledge in real analysis and graduate students interested in the area, it is also an introduction to a "dynamical way of thinking".

The questions studied here are dynamical as well as number theoretical in nature, and the answers are obtained with the help of ergodic theory. Attention is focused on concepts like measure-preserving, ergodicity, natural extension, induced transformations, and entropy. These concepts are then applied to familiar expansions to obtain old and new results in an elegant and straightforward manner. What it means to be ergodic and the basic ideas behind ergodic theory will be explained along the way. The subjects covered vary from classical to recent, which makes this book appealing to researchers as well as students.

  • Chapters
  • Chapter 1. Introduction
  • Chapter 2. Variations on a theme (Other expansions)
  • Chapter 3. Ergodicity
  • Chapter 4. Systems obtained from other systems
  • Chapter 5. Diophantine approximation and continued fractions
  • Chapter 6. Entropy
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.