STATISTICAL SURFACE DISTRIBUTIONS FOR CONSTANT-ENERGY ENSEMBLES

The dynamical properties of the surface density of a constant-energy e nsemble are discussed. An equilibrium surface density is introduced an d used to calculate single- and multivariable distributions for first- and second-order Hamiltonians. In particular the distribution of inter sections in a Poincare surface of section for a second-order Hamiltoni an is obtained. The results an applied to the special case of one simp le harmonic oscillator, two uncoupled simple harmonic oscillators, and the Henon-Heiles system.