English

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

Dynamical Systems 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.math/0006229,
  title  = {Adiabatic limits of closed orbits for some Newtonian systems in R^n},
  author = {Andrea Malchiodi},
  journal= {arXiv preprint arXiv:math/0006229},
  year   = {2007}
}

Comments

28 pages