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Adiabatic limits of closed orbits for some Newtonian systems in R^n

Andrea Malchiodi
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Abstract

We deal with a Newtonian system like x'' + V'(x) = 0. We suppose that V: \R^n \to \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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Andrea Malchiodi. 2000-06-30. Adiabatic limits of closed orbits for some Newtonian systems in R^n. https://arxiv.org/abs/math/0006229

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