We consider planar triangular maps that preserve certain fibration of the plane. We assume that there exists an invariant attracting fiber and we study the limit dynamics of those points in the basin of attraction of this invariant fiber, assuming that either it contains a global attractor, or it is filled by fixed or 2-periodic points. We apply our results to several examples.
Cima, A.; Gasull, A.; Mañosa, V. Basin of attraction of triangular maps with applications. "Journal of difference equations and applications", Març 2014, vol. 20, núm. 3, p. 423-437.