Title: Ergodic theory : with a view towards number theory /
Authors: Einsiedler, Manfred.; Ward, Thomas.
Publisher: Springer-Verlag,
Year: 2011
Subjects: Ergodic theory.
Abstract: This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. It describes some recent applications to number theory, and goes beyond the standard texts in this topic.
Contents: Motivation -- Ergodicity, recurrence and mixing -- Continued fractions -- Invariant measures for continuous maps -- Conditional measures and algebras -- Factors and joinings -- Furstenberg's proof of Szemerédi's theorem -- Actions of locally compact groups -- Geodesic flow on quotients of the hyperbolic plane -- Nilrotation -- More dynamics on quotients of the hyperbolic plane.