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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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Advances in Astronomy |
| Online Access: | http://dx.doi.org/10.1155/2021/6665238 |
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| author | Euaggelos E. Zotos Fredy L. Dubeibe A. Riaño-Doncel |
| author_facet | Euaggelos E. Zotos Fredy L. Dubeibe A. Riaño-Doncel |
| author_sort | Euaggelos E. Zotos |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-3f699d611ca041378a01ef4682e4ae64 |
| institution | Kabale University |
| issn | 1687-7969 1687-7977 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Astronomy |
| spelling | doaj-art-3f699d611ca041378a01ef4682e4ae642025-02-03T06:12:31ZengWileyAdvances in Astronomy1687-79691687-79772021-01-01202110.1155/2021/66652386665238Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles PotentialEuaggelos E. Zotos0Fredy L. Dubeibe1A. Riaño-Doncel2Department of Physics, School of Science, Aristotle University of Thessaloniki, Thessaloniki GR-541 24, GreeceFacultad de Ciencias Humanas y de la Educación, Universidad de los Llanos, Villavicencio, ColombiaFacultad de Ciencias Humanas y de la Educación, Universidad de los Llanos, Villavicencio, ColombiaThis 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 |
| 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 |
| title | 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_short | Fractal Basins of Convergence of a Seventh-Order Generalized Hénon–Heiles Potential |
| title_sort | fractal basins of convergence of a seventh order generalized henon heiles potential |
| url | http://dx.doi.org/10.1155/2021/6665238 |
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