Open AccessEscaping problem in the Hénon-Heiles system and numerical algorithms
Author(s) -
Zhao Hai-Jun,
Mingjing Du
Publication year - 2007
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.56.3827
Subject(s) - chaotic , function (biology) , algorithm , measure (data warehouse) , symplectic geometry , order (exchange) , statistical physics , physics , point (geometry) , computer science , mathematics , mathematical analysis , geometry , artificial intelligence , database , evolutionary biology , biology , finance , economics
We study the trajectories and escaping problem in the Hénon-Heiles system using a new fourth order symplectic algorithm and the Runge-Kutta-Fehlberg algorithm. Starting from the same initial pointwe found the distance between the two numerical trajectories calculated by the two algorithms increases exponentially in time in the chaotic region. We show this result can be used to measure chaos. We also calculate the escape rate as a function of energy above threshold in the Hénon-Heiles system. The results calculated with two different algorithms agree very well.