Registry · Proposition
IV.P149
tau-effective
formalized
IV.P149 — Quasi-ergodicity
The irrationality of iota_tau ensures that double rotation on T^2 by angle 2*pi*iota_tau is quasi-ergodic: the orbit of any point is dense in T^2. This follows because iota_tau is irrational (indeed transcendental), so no discrete lattice structure truncates the fiber dynamics.
Book IV
Part 1
Ch. 4