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Ergodic Theory - with a view towards Number Theory (Paperback, 2011 ed.)
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Ergodic Theory - with a view towards Number Theory (Paperback, 2011 ed.)
Series: Graduate Texts in Mathematics, 259
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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.
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