Graduate Texts in Mathematics

Ergodic Theory

with a view towards Number Theory

Authors: Einsiedler, Manfred, Ward, Thomas

  • 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 for problems
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About this Textbook

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.

Reviews

From the reviews:

“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)

“The book under review is an introductory textbook on ergodic theory, written with applications to number theory in mind. … it aims both to provide the reader with a solid comprehensive background in the main results of ergodic theory, and of reaching nontrivial applications to number theory. … The book should also be very appealing to more advanced readers already conducting research in representation theory or number theory, who are interested in understanding the basis of the recent interaction with ergodic theory.” (Barak Weiss, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 114, 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)

“The book contains a presentation of the ergodic theory field, focusing mainly on results applicable to number theory. … of interest for researchers, specialists, professors and students that work within some other areas than precisely the ergodic theory. … ‘Ergodic Theory. With a view toward number theory’ is now an indispensable reference in the domain and offers important instruments of research for other theoretical fields.” (Adrian Atanasiu, Zentralblatt MATH, Vol. 1206, 2011)


Table of contents (11 chapters)

  • Motivation

    Einsiedler, Manfred (et al.)

    Pages 1-12

  • Ergodicity, Recurrence and Mixing

    Einsiedler, Manfred (et al.)

    Pages 13-68

  • Continued Fractions

    Einsiedler, Manfred (et al.)

    Pages 69-95

  • Invariant Measures for Continuous Maps

    Einsiedler, Manfred (et al.)

    Pages 97-119

  • Conditional Measures and Algebras

    Einsiedler, Manfred (et al.)

    Pages 121-151

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-0-85729-021-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.95
price for USA
  • ISBN 978-0-85729-020-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $74.95
price for USA
  • ISBN 978-1-4471-2591-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Ergodic Theory
Book Subtitle
with a view towards Number Theory
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
259
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-021-2
DOI
10.1007/978-0-85729-021-2
Hardcover ISBN
978-0-85729-020-5
Softcover ISBN
978-1-4471-2591-4
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XVII, 481
Topics