2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/15702In 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.11 pages Latex, to appear in Dynamical Systems: From Crystal to Chaos, World Scientific, 1999Chaotic Dynamicstext