Manfred Einsiedler: Ergodic Theory | Buch

Cover: 9780857290205 | Ergodic Theory | with a view towards Number Theory | Buch | xvii

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Beschreibung

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.

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence.

Zusammenfassung

With a rigorous development of basic ergodic theory and homogeneous dynamics, no background in Ergodic theory or Lie theory is assumed Offers both complete and motivated treatments of Weyl and Szemeredi theorems Provides a number of exercises and hints to problems

Includes supplementary material: [...]

Inhaltsverzeichnis

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

Erscheinungsjahr:	2010
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Graduate Texts in Mathematics
Inhalt:	xvii 481 S. 52 Farbfotos 104 Fotos
ISBN-13:	9780857290205
ISBN-10:	0857290207
Sprache:	Englisch
Herstellernummer:	80020504
Einband:	Gebunden
Autor:	Einsiedler, Manfred Ward, Thomas
Hersteller:	Springer-Verlag GmbH Springer-Verlag London Ltd.
Abbildungen:	52 schwarz-weiße und 52 farbige Abbildungen
Maße:	241 x 167 x 33 mm
Von/Mit:	Manfred Einsiedler (u. a.)
Erscheinungsdatum:	23.09.2010
Gewicht:	0,875 kg

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