# N-body Dynamics on Closed Surfaces. The Axioms of Mechanics

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Stefanella Boatto

created by risa on 18 Dec 2015

22 dec 2015
-- 09:30

Aula 34, Dip. Scienze Statistiche, Università "La Sapienza", Roma

**Abstract.**

One of the today's challenges is the formulation of the N-body and N-vortex dynamics on Riemann surfaces. In this talk we show how the two problems are strongly related one another when looking at them from the point of view of the intrinsic geometry of the surface where the dynamics takes place. Given a surface M of metric g, the distribution of matter S on M, we deduce the dynamics of the masses and some of its properties. Among other things, we find that in the plane the two masses problem does not obeys to the known Kepler laws. Moreover, Newton's Laws are not longer verified on closed surfaces with variable curvature. (Joint work with D. Dritschel and R. Schaefer).