Ergodic Theory

with a view towards Number Theory

  • Manfred Einsiedler
  • Thomas Ward

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Manfred Einsiedler, Thomas Ward
    Pages 1-12
  3. Manfred Einsiedler, Thomas Ward
    Pages 13-68
  4. Manfred Einsiedler, Thomas Ward
    Pages 69-95
  5. Manfred Einsiedler, Thomas Ward
    Pages 97-119
  6. Manfred Einsiedler, Thomas Ward
    Pages 121-151
  7. Manfred Einsiedler, Thomas Ward
    Pages 153-169
  8. Manfred Einsiedler, Thomas Ward
    Pages 171-230
  9. Manfred Einsiedler, Thomas Ward
    Pages 231-275
  10. Manfred Einsiedler, Thomas Ward
    Pages 277-330
  11. Manfred Einsiedler, Thomas Ward
    Pages 331-345
  12. Manfred Einsiedler, Thomas Ward
    Pages 347-402
  13. Back Matter
    Pages 403-481

About this book

Introduction

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.

Keywords

Ergodic theory Homogenous spaces Measure rigidity Number theory

Authors and affiliations

  • Manfred Einsiedler
    • 1
  • Thomas Ward
    • 2
  1. 1.Departement MathematikETH Zürich Departement MathematikZürichSwitzerland
  2. 2.School of MathematicsUniversity of East Anglia School of MathematicsNorwichUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-021-2
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-85729-020-5
  • Online ISBN 978-0-85729-021-2
  • About this book