Trajectories of the images in binary microlensing

We study in detail the trajectories followed by single images during binary microlensing events. Starting from perturbative resolutions of the lens equation, we explore the full parameter space by continuity arguments. We see that the images created during the caustic crossing can recombine with the others in different ways. This leads to a new classification of the microlensing events according to the behaviour of the images. We show that the images involved in these combinations depend on the folds that are crossed at the entry and at the exit from the caustic. Non-trivial trajectories can be classified into four main types. Some consequences for the motion of the center of light of the source in astrometric measurements are also examined.