Attractors stuck on to invariant subspaces

This note considers some attractors for maps with invariant subspaces. An example is presented with a family of attractors (displaying on-off intermittency) that intersect their reflections along a reflection plane. This is a robust example of (a) an attractor that is ''stuck on'' to its basin boundary and (b) two attractors in a symmetric system that collide at a reflection plane without merging. A further example with D-3 symmetry having attractors stuck on to more than one reflection plane is presented.