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 positions of the points of equilibrium, while we also obtain their linear st...

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Main Authors:	Euaggelos E. Zotos, Fredy L. Dubeibe, A. Riaño-Doncel
Format:	Article
Language:	English
Published:	Hindawi Limited 2021-01-01
Series:	Advances in Astronomy
Online Access:	http://dx.doi.org/10.1155/2021/6665238

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spelling	doaj-3f699d611ca041378a01ef4682e4ae642021-07-26T00:34:21ZengHindawi LimitedAdvances in Astronomy1687-79772021-01-01202110.1155/2021/6665238Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles PotentialEuaggelos E. Zotos0Fredy L. Dubeibe1A. Riaño-Doncel2Department of PhysicsFacultad de Ciencias Humanas y de la EducaciónFacultad de Ciencias Humanas y de la EducaciónThis 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 positions 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.http://dx.doi.org/10.1155/2021/6665238
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Euaggelos E. Zotos Fredy L. Dubeibe A. Riaño-Doncel
spellingShingle	Euaggelos E. Zotos Fredy L. Dubeibe A. Riaño-Doncel Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles Potential Advances in Astronomy
author_facet	Euaggelos E. Zotos Fredy L. Dubeibe A. Riaño-Doncel
author_sort	Euaggelos E. Zotos
title	Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles Potential
title_short	Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles Potential
title_full	Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles Potential
title_fullStr	Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles Potential
title_full_unstemmed	Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles Potential
title_sort	fractal basins of convergence of a seventh-order generalized hénon–heiles potential
publisher	Hindawi Limited
series	Advances in Astronomy
issn	1687-7977
publishDate	2021-01-01
description	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 positions 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.
url	http://dx.doi.org/10.1155/2021/6665238
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Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles Potential

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