Ergodic theory, like probability theory, is based on general notions of measure theory. Its initial development was motivated by problems of statistical physics. A central concern of ergodic theory is …

Von Neumann’s Mean Ergodic Theorem deals with convergence of operators in L2. We would actually like to have a pointwise result, which unfortunately doesn’t follow from the L2 convergence.

Ergodic theory is a part of the theory of dynamical systems. At its simplest form, a dynamical system is a function T defined on a set X. The iterates of the map are defined by induction T0 := id, Tn := T …

One of the fundamental questions in ergodic theory is: when are two measurable dynamical systems isomorphic? In this section we will study basic properties of these dynamical systems:

We give a very brief introduction to the ergodic theorem as well as the subad-ditive ergodic theorem. For more, see e.g. [Dur10, Chapter 7]. The context for ergodic theory is stationary sequences, as defined …

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.

Ergodic theory is the study of systems possessing ergodicity. Ergodic systems occur in a broad range of systems in physics and in geometry.

Mar 25, 2026 · Ergodic theory can be described as the statistical and qualitative behavior of measurable group and semigroup actions on measure spaces. The group is most commonly N, R, R-+, and Z.

Indefinite Quadratic Forms and Oppenheim's Conjecture ....

Apr 13, 2011 · The Ergodic Hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are ergodicity, weak mixing, strong …