Unwrapping trajectories of a quasi-periodic forced oscillator can give maps of the real line with SNA

We start from a simple model of quasi-periodic forced oscillator and show how it is possible to find corresponding maps of the two dimension torus. One of these constructions is frequently used to analyse the apparition of strange non-chaotic attractors (SNA in brief). SNA are complex attractors, their trajectories seem to be chaotic but without the sensitivity to initial conditions. Some trajectories can be unwrapped from the torus giving a simple iteration of the real line. It leads us to suppose that iterations from a simple continuous increasing map with quasi-periodic displacement can exhibit SNA.