Slow-fast Dynamics Generated by Noninvertible Plane Maps

The present paper focuses on the two time scale dynamics generated by 2D polynomial noninvertible maps T of (Z0−Z2) and (Z1−Z3−Z1) types. This symbolism, specific to noninvertible maps, means that the phase plane is partitioned into zones Zk, where each point possesses the k real rank-one preimages. Of special interest here is the structure of slow and fast motion sets of such maps. The formation mechanism of a stable invariant close curve through the interaction of fast and slow dynamics, as well as its transformation into a canard are studied. A few among the plethora of chaotic attractors and chaotic transients produced by such maps are described as well.