Quasi-invariant attractors of piecewise isometric systems

We describe new examples of global attractors arising in planar piecewise rotations with two convex atoms. The dynamics inside these attractors is proved to be equivalent to that from models of digital filters.
We also discuss some subtleties on the definition of piecewise isometric attractors and their properties, motivated not only by our new examples but also by others existing in the literature. More precisely, we require a minimality condition so that uniqueness is guaranteed and also, we establish equivalent forms of attractivity under some regularity assumption. The notion of quasi-invariance is introduced as it proves to be a suitable concept in the context of planar piecewise rotations.