We deal with a Newtonian system like x over dots + V'(x) = 0. We suppose that V : R-n --> R possesses an (n - 1)-dimensional compact manifold M of critical points, and we prove the existence of arbitrarily slow periodic orbits. When the period tends to infinity these orbits, rescaled in time, converge to some closed geodesics on M.
Adiabatic limits of closed orbits for some Newtonian systems in R-n
Malchiodi, Andrea
2001
Abstract
We deal with a Newtonian system like x over dots + V'(x) = 0. We suppose that V : R-n --> R possesses an (n - 1)-dimensional compact manifold M of critical points, and we prove the existence of arbitrarily slow periodic orbits. When the period tends to infinity these orbits, rescaled in time, converge to some closed geodesics on M.File in questo prodotto:
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