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

Citation
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
Citations number
20
Categorie Soggetti
Physycs, Mathematical","Phsycs, Fluid & Plasmas
ISSN journal
1063651X
Volume
49
Issue
4
Year of publication
1994
Part
A
Pages
2549 - 2558
Database
ISI
SICI code
1063-651X(1994)49:4<2549:FDTSIT>2.0.ZU;2-9
Abstract
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.