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We derive a first order formalism for solving the scattering of point sourcesin (2+1) gravity with negative cosmological constant. We show that theirphysical motion can be mapped, with a polydromic coordinate transformation, toa trivial motion, in such a way that the point sources move as time-likegeodesics (in the case of particles) or as space-like geodesics (in the case ofBTZ black holes) of a three-dimensional hypersurface immersed in afour-dimensional Minkowskian space-time, and that the two-body dynamics issolved by two invariant masses, whose difference is simply related to the totalangular momentum of the system.Comment: 15 pages, LaTeX, no figure

INTEGRABILITY OF THE N-BODY PROBLEM IN (2+1)-AdS GRAVITY