Hyperbolic Orbits for a Class of Singular Hamiltonian Systems
  The existence of hyperbolic orbits is proved for a class of singular Hamiltonian systems $\ddot{u}(t)+\nabla V(u(t))=0$ by taking limit for a sequence of periodic solutions which are the variational minimizers of Lagrangian actions. 
Donglun Wu and Shiqing Zhang
math.CA