Fractal Fourier spectra of Cherry flows

Flows on the 2-torus with points of equilibrium are considered. Numerical observations suggest that, for the case of trajectories with irrational rotation numbers, power spectra are singular continuous. Dynamics is adequately represented by a symbolic sequence built from four symbols with the help of a substitution rule. This rule effectively takes into account the slowing down of the motion during passages near the saddle point and the superexponential scaling of returns onto a secant line.