Introduction to Ergodic Theory

Ergodic theory traces its origins to questions in statistical mechanics about understanding motion in dynamical systems, with the motion of the planets around the sun being one of the earliest examples of a dynamical system. Since that time ergodic theory has grown into a central area of mathematics and has interacted and contributed to many areas of mathematics including harmonic analysis, number theory, probability, operator algebras, geometry, and topology. Ergodic theory is characterized by its use of measure-theoretic and probabilistic tools to study dynamical systems. At the same time, topological, differentiable, and operator tools arise in a natural way and this volume has articles that address topological and differentiable dynamics and their connections with ergodic theory. For a more detailed description of ergodic theory and its role in the modern mathematics, we refer to “Introduction to Ergodic Theory,” by Bryna Kra, from the first edition of this collection.

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