Ergodic theory : with a view towards number theory

書誌事項

Ergodic theory : with a view towards number theory

Manfred Einsiedler, Thomas Ward

(Graduate texts in mathematics, 259)

Springer, c2011

  • : pbk

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注記

Includes bibliographical references (p. 447-462) and indexes

内容説明・目次

内容説明

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.

目次

Motivation.- Ergodicity, Recurrence and Mixing.- Continued Fractions.- Invariant Measures for Continuous Maps.- Conditional Measures and Algebras.- Factors and Joinings.- Furstenberg's Proof of Szemeredi's Theorem.- Actions of Locally Compact Groups.- Geodesic Flow on Quotients of the Hyperbolic Plane.- Nilrotation.- More Dynamics on Quotients of the Hyperbolic Plane.- Appendix A: Measure Theory.- Appendix B: Functional Analysis.- Appendix C: Topological Groups

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詳細情報

  • NII書誌ID(NCID)
    BB03590761
  • ISBN
    • 9780857290205
    • 9781447125914
  • LCCN
    2010936100
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    London
  • ページ数/冊数
    xvii, 481 p.
  • 大きさ
    25 cm
  • 分類
  • 親書誌ID
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