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Threshold law for escaping from the Hénon-Heiles system
Phys. Rev. E 76, 027201 – Published 22 August, 2007
DOI: https://doi.org/10.1103/PhysRevE.76.027201
Abstract
We report a theoretical study of the escape rates of the Hénon-Heiles system above threshold. An analytic formula for the escape rate as a function of energy is presented. 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 Hénon-Heiles system follows exponential laws. We extracted the escape rates from the time dependence of particle numbers in the Hénon-Heiles potential. The extracted escape rates agree with the analytic result. Close to threshold we find the rate can be written as a series expansion, the first term of this expansion is .
Article Text
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