On the Novikov problem for superposition of periodic potentials

We consider the Novikov problem, namely, the problem of describing the level lines of quasiperiodic functions on the plane, for a special class of potentials that have important applications in the physics of two-dimensional systems. Potentials of this type are given by a superposition of periodic potentials and represent quasiperiodic functions on a plane with four quasiperiods. Here we study an important special case when the periodic potentials have the same rotational symmetry. In the generic case, their superpositions have chaotic'' open level lines, which brings them close to random potentials. At the same time, the Novikov problem has interesting features also for magic’’ rotation angles, which lead to the emergence of periodic superpositions.