At a=0.8 the effects of the nonintegrability are more evident:
The chaos is more evident, although the extent of a chaotic orbit is still limited to bands by those of the original tori that survive: these tori form a barrier to the chaotic orbits. You should also be able to find that some of the "elliptical orbits" surrounding the locked orbits (again the ones with winding numbers about the locked orbits close to simple rationals) have themselves broken down to island chains of elliptical orbits with chaotic orbits in the hyperbolic regions between them.