  We consider some planar triangular maps. These maps 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. Finally, we apply our
results to a variety of examples, from particular cases of triangular systems
to some planar quasi-homogeneous maps, and some multiplicative and additive
difference equations, as well.

Dynamical Systems