Nonhyperbolic persistent attractors near the Morse-Smale boundary were discussed. Morse-Smale systems constituted an open set of dynamically or structurally stable elements. The presence in the cycle of just one branch of the unstable manifold of the singularity is important to obtain the desired results. It was concluded that the set of parameters where the critical values are not dense is a zero Lebesgue measure set.
Muñoz Morales, E. M., San Martín Rebolledo, B., & Vera Valenzuela, J. A. (2003). Nonhyperbolic persistent attractors near the Morse-Smale boundary. Annales de l’Institut Henri Poincare (C) Analyse Non Lineaire, 20(5), 867–888. https://doi.org/10.1016/S0294-1449(03)00015-5