FROM DYNAMICS TO STATISTICAL-MECHANICS IN THE HENON-HEILES MODEL - STATISTICAL-MECHANICS

The dynamical and statistical properties of 100 trajectories on the cr itical energy surface of the Henon-Heiles model are investigated using statistical and time ensembles and Poincare surfaces of section. The statistical ensembles for chaotic and nonchaotic orbits relax reversib ly to statistical equilibrium at different rates. The equilibrium coar se-grained distribution functions for the position and velocity coordi nates in the chaotic orbits are very similar to the corresponding chao tic time-ensemble distributions and the distributions predicted by the Statistical Mechanics of an isolated system. The statistical-ensemble and time-ensemble distributions in the nonchaotic orbits are also sim ilar but quite different from the chaotic distributions. The relations hip between the nonchaotic distribution functions and the quasi-isolat ing integral is discussed.