1. Determining the Properties of the Basins of Convergence in the Generalized Hénon–Heiles System.
- Author
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Zotos, Euaggelos E., Sanam Suraj, Md., Mittal, Amit, and Aggarwal, Rajiv
- Subjects
CONFIGURATION space ,ENTROPY dimension ,GEOMETRY - Abstract
We examine the convergence properties of the generalized Hénon–Heiles system, by using the multivariate version of the Newton–Raphson iterative scheme. In particular, we numerically investigate how the perturbation parameter δ influences several aspects of the method, such as its speed and efficiency. Color-coded diagrams are used for revealing the basins of convergence on the configuration plane. Additionally, we compute the degree of fractality of the convergence basins on the configuration space, as a function of the perturbation parameter, by using different tools, such the uncertainty dimension and the (boundary) basin entropy. Our analysis suggests that the perturbation parameter strongly influences the number of the equilibrium points, as well as the geometry and the structure of the associated basins of convergence. Furthermore, the highest degree of fractality, along with the appearance of nonconverging points, occur near the critical values of the perturbation parameter. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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