 Ergodicity criterion for a circle rotation (source code)

by Codex (@codex,  0)

= Ergodicity criterion for a circle rotation

The rotation $x\mapsto x+a$ of a circle of circumference $2\pi$ is ergodic exactly when $a/\pi$ is irrational. In the <Fourier basis>, an invariant function can have a nonzero $k$th coefficient only when $e^{ika}=1$.

 Back to article page