Dynamical analysis of bounded and unbounded orbits in a generalized Hénon-Heiles system

Abstract

The Hénon-Heiles potential was first proposed as a simplified version of the gravitational potential experimented by a star in the presence of a galactic center. Currently, this system is considered a paradigm in dynamical systems because despite its simplicity exhibits a very complex dynamical behavior. In the present paper, we perform a series expansion up to the fifth-order of a potential with axial and reflection symmetries, which after some transformations, leads to a generalized Hénon-Heiles potential. Such new system is analyzed qualitatively in both regimes of bounded and unbounded motion via the Poincaré sections method and plotting the exit basins. On the other hand, the quantitative analysis is performed through the Lyapunov exponents and the basin entropy, respectively. We find that in both regimes the chaoticity of the system decreases as long as the test particle energy gets far from the critical energy. Additionally, we may conclude that despite the inclusion of higher order terms in the series expansion, the new system shows wider zones of regularity (islands) than the ones present in the Hénon-Heiles system.

7 pages, 5 figures

References in corpus (4)

• Basin entropy: a new tool to analyze uncertainty in dynamical systems
• Chaotic dynamics and fractal structures in experiments with cold atoms
• Controlling unpredictability in the randomly driven Hénon-Heiles system
• An overview of the escape dynamics in the Henon-Heiles Hamiltonian system

Cited by in corpus (6)

• Basins of convergence of equilibrium points in the generalized Henon-Heiles system
• Unpredictability and basin entropy
• Measure synchronization in interacting Hamiltonian systems: A brief review
• On the dynamics of a seventh-order generalized Hénon-Heiles potential
• Fractal basins of convergence of a seventh-order generalized Hénon-Heiles potential
• Orbital dynamics in realistic galaxy models: NGC 3726, NGC 3877 and NGC 4010