On a dynamical system related to fluid mechanics

We introduce a dynamical system strictly related to fluid mechanics and similar to the classical N point vortex system. In the first part we analyze the qualitative behavior of the time evolution and in particular we show the properties of collapse and chaoticity. In the second part of the paper we investigate the relation of the dynamical system with a system of N concentrated large enough smoke rings in an incompressible and inviscid fluid, with axial symmetry and without swirl. We prove the rigorous connection between the two models at time zero for any N. The extension of the same result to any time is obtained only for a smoke ring alone, while for the general case it is just a matter of conjecture. Received June 1998; Revised November 1998