 Ergodic theory

Ergodic theory studies the long-time statistical behaviour of measure-preserving transformations.

Ergodic theory is a branch of mathematics that studies the long-term average behavior of dynamical systems. It originated in the context of statistical mechanics and has applications in various fields, including probability theory, statistics, and even areas of physics and number theory. At its core, ergodic theory investigates how a system evolves over time and how its states are distributed in space.