Bi. Henry et J. Grindlay, FROM DYNAMICS TO STATISTICAL-MECHANICS IN THE HENON-HEILES MODEL - DYNAMICS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 49(4), 1994, pp. 2549-2558
The equations of motion of the Henon-Heiles model have been numericall
y integrated for 100 different starting conditions on the critical ene
rgy surface E = 1/6. The truncation error in the data was monitored us
ing the separation in phase space of two numerical histories with the
same initial conditions, based on different time steps, h = 2(-13) and
h' = 2(-14). From the data for which the truncation error is less tha
n 1% it is found that the 100 histories fall into three categories, (a
) regular (or quasiperiodic), (b) irregular (or chaotic), and (c) regu
lar-irregular. The three-dimensional phase space portraits prove to be
the most useful tool in distinguishing between regular and irregular
behavior. In category (c) the orbit switches reversibly from (to) regu
lar to (from) irregular behavior. The data suggest that all 100 orbits
, followed for long enough times, will show regular-irregular behavior
and moreover the phase points in these orbits will spend, on average,
equal amounts of time in the quasiperiodic and chaotic regimes.