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  3. Ergodic Theory of Numbers
  • Cited by 114
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    • Publisher:
      Mathematical Association of America
      Publication date:
      Invalid date
      June 2002
      ISBN:
      9780883850343
      DOI:
      https://doi.org/10.5948/UPO9781614440277
      Dimensions:
      Weight & Pages:
      00kg,
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Number Theory
      Series:
      Carus Mathematical Monographs
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    Subjects:
    Mathematics, Number Theory
    Series:
    Carus Mathematical Monographs
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    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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