Transient periodic behaviour related to a saddle-node bifurcation

The authors investigate transient periodic orbits of dissipative invertible maps of R 2 . Such orbits exist just before, in parameter space, a saddle-node pair is formed. They 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 C 2 -of the stable manifolds of the two complex saddles in C 2 that bifurcate ino the real saddle-node pair.