Transient periodic behaviour related to a saddle-node bifurcation

We investigate transient periodic orbits of dissipative invertible maps of R2. Such orbits exist just before, in parameter space, a saddle-node pair is formed. We obtain numerically and analytically simple scaling laws for the duration of the transient, and for the region of initial conditions which evolve into transient periodic orbits. An estimate of this region is then obtained by the construction-after extension of the map to C2-of the stable manifolds of the two complex saddles in C2 that bifurcate into the real saddle-node pair.