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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.
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.
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)