Supersymmetry in classical mechanics

The concept of supersymmetry extended to classical mechanics relates one-pa rameter families of Hamiltonians H( xi,x,p)=p(2) + V(xi,x), such that the m apping from the phase space of H(xi(1),x,p) to that of H(xi(2),x,p) preserv es time-evolution and conserves total energy; as a result, equal-energy per iodic orbits in the two have the same period. While t-evolution is a contac t transformation generated by H, xi-evolution is a generalized contact tran sformation generated by a function K, and preserves phase volume except for a point sink (source) as xi increases (decreases). Closed-form solutions o f xi-evolution include several well-known examples. (C) 2000 Elsevier Scien ce B.V. All rights reserved.