Abstract
The Hénon-Heiles system is a 2-dimensional axisymmetric Hamiltonian system that was first formed to determine the third integral of motion in galactic dynamics. After its inception, it has become a paradigm in dynamical systems due to its apparent simplicity but extremely complicated dynamical behavior. In this paper, we perform a series expansion up to the seventh order of a general potential with axial and reflection symmetries. After some transformations, this becomes a generalized Hénon-Heiles (GHH) system where we separate the fifth and seventh-order terms. We qualitatively analyze this system for energies near the threshold between bounded and unbounded motion with Poincaré sections and quantitatively analyze with Lyapunov exponents. We find that particles far from the critical energy demonstrate less chaos. Additionally, the fifth-order term creates more regularity while the seventh-order term does the opposite.
Recommended Citation
Madhukara, Nandana
(2024).
(R2078) Analyzing the Effects of Fifth and Seventh Order Terms in a Generalized Henon-Heiles Potential,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 19,
Iss.
2, Article 3.
Available at:
https://digitalcommons.pvamu.edu/aam/vol19/iss2/3