Scaling in activated escape of underdamped systems
  Noise-induced escape from a metastable state of a dynamical system is studied close to a saddle-node bifurcation point, but in the region where the system remains underdamped. The activation energy of escape scales as a power of the distance to the bifurcation point. We find two types of scaling and the corresponding critical exponents. 
M.I. Dykman, I.B. Schwartz, and M. Shapiro