Ergodic Theory

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

From the reviews:

"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)

"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)

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 contemporarydevelopments in mathematics."