Morse Theory for geodesics in singular conformal metrics
  Motivated by the use of degenerate Jacobi metrics for the study of brake orbits and homoclinics, we develop a Morse theory for geodesics in conformal metrics having conformal factors vanishing on a regular hypersurface of a Riemannian manifold. 
R. Giamb\`o, F. Giannoni, P. Piccione
math.DS math-ph math.DG math.MP