Characterization of the set of "ergodic directions" in the Novikov's problem of quasi-electrons orbits in normal metals

Novikov's problem of semiclassical orbits of quasi-electrons in a normal metal leads to a correspondance between 3-ply periodic functions in R and fractals in R P^2. These fractals are the complement of infinitely many open sets labeled by integer 2-cycles of T^3. Here we present a characterization of the fractal points in terms of the open sets labels.