Ergodic Theory: with a view towards Number Theory Graduate Texts in Mathematics, Vol. 259 Graduate Texts in Mathematics, 259 | First Edition Edition

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Details about Ergodic Theory: with a view towards Number Theory Graduate Texts in Mathematics, Vol. 259 Graduate Texts in Mathematics, 259:

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.

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With over 30 years of teaching, I have the honor and pleasure to say that I have former students – who are doctors, scientists, Engineers, and business men & women - who still keep in touch and even come to visit. Some keep in-touch even from other countries and many call or Skype; and some call for help and advice. Read more

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