3 0 Ju n 20 00 Adiabatic limits of closed orbits for some Newtonian systems in R n

Abstract

We deal with a Newtonian system like ẍ+V (x) = 0. We suppose that V : R → R possesses an (n− 1)-dimensional compact manifold M of critical points, and we prove the existence of arbitrarity slow periodic orbits. When the period tends to infinity these orbits, rescaled in time, converge to some closed geodesics on M . 

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