  In neuroscience, optics and condensed matter there is ample physical evidence
for multistable dynamical systems, that is, systems with a large number of
attractors. The known mathematical mechanisms that lead to multiple attractors
are homoclinic tangencies and stabilization, by small perturbations or by
coupling, of systems possessing a large number of unstable invariant sets. A
short review of the existent results is presented, as well as two new results
concerning the existence of a large number of stable periodic orbits in a
perturbed marginally stable dissipative map and an infinite number of such
orbits in two coupled quadratic maps working on the Feigenbaum accumulation
point.
