Escape Rates of the Hénon-Heiles System
| dc.creator | Zhao, H. J. | |
| dc.creator | Du, M. L. | |
| dc.date | 2007-01-15 | |
| dc.date.accessioned | 2026-07-07T07:41:04Z | |
| dc.date.available | 2026-07-07T07:41:04Z | |
| dc.description | A particle in the Hénon-Heiles potential can escape when its energy is above the threshold value $E_{th}={1/6}$. We report a theoretical study on the the escape rates near threshold. We derived an analytic formula for the escape rate as a function of energy by exploring the property of chaos. We also simulated the escaping process by following the motions of a large number of particles. Two algorithms are employed to solve the equations of motion. One is the Runge-Kutta-Fehlberg method, and another is a recently proposed fourth order symplectic method. Our simulations show the escape of H$\mathrm{\acute{e}}$non-Heiles system follows exponential laws. We extracted the escape rates from the time dependence of particle numbers in the H$\mathrm{\acute{e}}$non-Heiles potential. The extracted escape rates agree with the analytic result. | |
| dc.description | 10 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/nlin/0701028 | |
| dc.identifier | http://arxiv.org/abs/nlin/0701028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121970 | |
| dc.subject | Chaotic Dynamics | |
| dc.title | Escape Rates of the Hénon-Heiles System | |
| dc.type | text |