Ergodic Theory: With a View Towards Number Theory: 259 - Rilegato

Einsiedler, Manfred; Ward, Thomas

Rilegato

ISBN 10: 0857290207 ISBN 13: 9780857290205

Casa editrice: Springer Verlag, 2010

Riassunto

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.

Su questo libro

Recensione:

The book is an introduction to ergodic theory and dynamical systems. ... The book is intended for graduate students and researchers with some background in measure theory and functional analysis. Definitely, it is a book of great interest for researchers in ergodic theory, homogeneous dynamics or number theory. --Antonio Díaz-Cano Ocaña, The European Mathematical Society, January, 2014

A book with a wider perspective on ergodic theory, and yet with a focus on the interaction with number theory, remained a glaring need in the overall context of the development of the subject. ... The book under review goes a long way in fulfilling this need. ... it covers a good deal of conventional ground in ergodic theory ... . a very welcome addition and would no doubt inspire interest in the area among researchers as well as students, and cater to it successfully. --S. G. Dani, Ergodic Theory and Dynamical Systems, Vol. 32 (3), June, 2012

This introductory book, which goes beyond the standard texts and allows the reader to get a glimpse of modern developments, is a timely and welcome addition to the existing and ever-growing ergodic literature. ... This book is highly recommended to graduate students and indeed to anyone who is interested in acquiring a better understanding of contemporary developments in mathematics. --Vitaly Bergelson, Mathematical Reviews, Issue 2012 d

Contenuti:

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

Su questa edizione

• Editore: Springer Verlag
• Data di pubblicazione: 2010
• ISBN 10: 0857290207
• ISBN 13: 9780857290205
• Rilegatura: Copertina rigida
• Numero di pagine: 481