Signs of the cusps in binary lenses
  The cusps of the caustics of any gravitational lens model can be classified into positive and negative ones. This distinction lies on the parity of the images involved in the creation/destruction of pairs occurring when a source crosses a caustic in a cusp. In this paper, we generalize the former definition of the sign of the cusps. Then we apply it to the binary lens. We demonstrate that the cusps on the axis joining the two lenses are positive while the others are negative. To achieve our objective, we combine catastrophe theory, usually employed in the derivation of the properties of caustics, with perturbative methods, in order to simplify calculations and get readable results. Extensions to multiple lenses are also considered. 
Valerio Bozza