Ergodic Theory with a view towards Number Theory /

• Main Authors: Einsiedler, Manfred (Author), Ward, Thomas (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London : Imprint: Springer, 2011.
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Measure theory.; Number theory.; Dynamical Systems and Ergodic Theory.; Number Theory.; Measure and Integration.

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...

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.