arXiv subjects

A. Riaño-Doncel

Publications and source records attributed to A. Riaño-Doncel.

3 recordsLinked to original sources

arXiv2020

Fractal basins of convergence of a seventh-order generalized Hénon-Heiles potential

This article aims to investigate the points of equilibrium and the associated convergence basins in a seventh-order generalized Hénon-Heiles potential. Using the well-known Newton-Raphson iterator we numerically locate the position of the points of equilibrium, while we also obtain their linear stability. Furthermore, we demonstrate how the two variable parameters, entering the generalized Hénon-Heiles potential, affect the convergence dynamics of the system as well as the fractal degree of the basin diagrams. The fractal degree is derived by computing the (boundary) basin entropy as well as the uncertainty dimension.

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arXiv2018

Basins of convergence of equilibrium points in the generalized Henon-Heiles system

We numerically explore the Newton-Raphson basins of convergence, related to the libration points (which act as attractors of the convergence process), in the generalized Hénon-Heiles system (GHH). The evolution of the position as well as of the linear stability of the equilibrium points is determined, as a function of the value of the perturbation parameter. The attracting regions, on the configuration $(x,y)$ plane, are revealed by using the multivariate version of the classical Newton-Raphson iterative algorithm. We perform a systematic investigation in an attempt to understand how the perturbation parameter affects the geometry as well as of the basin entropy of the attracting domains. The convergence regions are also related with the required number of iterations.

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arXiv2018

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

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.

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