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We present an algebraic map (MAMA) for the dynamical and collisionalevolution of a planetesimal swarm orbiting the main star of a tight binarysystem (TBS). The orbital evolution of each planetesimal is dictated by thesecular perturbations of the secondary star and gas drag due to interactionswith a protoplanetary disk. The gas disk is assumed eccentric with a constantprecession rate. Gravitational interactions between the planetesimals areignored. All bodies are assumed coplanar. A comparison with full N-bodysimulations shows that the map is of the order of 100 times faster, whilepreserving all the main characteristics of the full system.  In a second part of the work, we apply MAMA to the \gamma-Cephei, searchingfor friendly scenarios that may explain the formation of the giant planetdetected in this system. For low-mass protoplanetary disks, we find that alow-eccentricity static disk aligned with the binary yields impact velocitiesbetween planetesimals below the disruption threshold. All other scenariosappear hostile to planetary formation.

MAMA: An Algebraic Map for the Secular Dynamics of Planetesimals in Tight Binary Systems