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Ergodic Theory with a view towards Number Theory

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 sta...

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Bibliographic Details
Main Authors: Einsiedler, Manfred, Ward, Thomas (Author)
Format: eBook
Language:English
Published: London Springer London 2011, 2011
Edition:1st ed. 2011
Series:Graduate Texts in Mathematics
Subjects:
Number Theory
Measure Theory
Dynamical Systems
Measure And Integration
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 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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