to y) are still sufficient to limit the chaotic orbits to bands.
At a=0.97 the last of the original tori disappear (although the subsidiary tori around the locked orbits remain). The winding number of this last "KAM torus" is the Golden Mean. You can try to find the last KAM torus by adjusting the initial condition to tune the winding number to this value (about 0.618).
This last torus (and the ones related to it by adding 2 to y) are still sufficient to limit the chaotic orbits to bands.