Perturbations of 8-attractors and births of satellite systems

We investigate the most basic two-dimensional generalizations of interval e xchange maps. We show that a recently discovered attracting piecewise rotat ion system with two atoms becomes repelling under a significant perturbatio n of one of the centers of rotation. However, small perturbations of this s ystem result in remarkable bifurcations into local attracting systems and t hey give birth to new satellite periodic cells. Bifurcations can be repeate d recursively and eventually lead to piecewise rotations with infinitely ma ny satellite periodic cells.