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  3. Ergodic Theory of Numbers
  • This book is no longer available to purchase from Cambridge Core
  • Cited by 100
Publisher:
Mathematical Association of America
Online publication date:
June 2014
Print publication year:
2002
Online ISBN:
9781614440277
DOI:
https://doi.org/10.5948/UPO9781614440277
Subjects:
Mathematics, Number Theory
Series:
Carus Mathematical Monographs
Information

Book description

Ergodic Theory of Numbers is an introduction to the ergodic theory behind common number expansion, 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.

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