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

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

2000-06-30

arxiv.org/abs/math/0006229v1

Mathematics

Dynamical Systems

28 pages

Scientific paper

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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