Pathway XXXI

TErgodic theory

A map that preserves measure. Ergodicity: invariant sets are trivial. Time average equals space average.

1. 01Measure-preserving mapsRotation of the circle by an irrational angle is ergodic: orbits densely wind, and never trap mass.4 min
2. 02MixingMixing is stronger than ergodicity: μ(A ∩ T⁻ⁿ B) → μ(A)μ(B). The past is forgotten.4 min