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The influence of third order terms on basins of convergence in the Hénon–Heiles type system.
- Source :
-
New Astronomy . Jul2022, Vol. 94, pN.PAG-N.PAG. 1p. - Publication Year :
- 2022
-
Abstract
- The effects of the third-order terms ɛ and η in the effective potential V = 1 2 (A x 2 + B y 2) − ɛ x 2 y − η y 3 , on the topology of Newton–Raphson basins of convergence (NRBoC), linked to the equilibrium points are presented. The evolution of the positions of the libration points as a function of the parameters ɛ and η is determined. The basins of convergence (BoC) in (x , y) plane, are unveiled by using the multivariate version of the Newton–Raphson (N-R) iterative scheme. In an attempt to analyse the effect of third order terms on the topology of the BoC as well as the basin entropy, we have performed a systematic numerical investigation. It is revealed that the third-order terms ɛ and η have significant effects on the topology of the BoC linked to the libration points. • The Hénon–Heiles type system has been studied. • The positions of libration points are illustrated. • The basins of convergence are unveiled. • The basins entropy are presented. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LAGRANGIAN points
*PSEUDOPOTENTIAL method
*NEWTON-Raphson method
*TOPOLOGY
Subjects
Details
- Language :
- English
- ISSN :
- 13841076
- Volume :
- 94
- Database :
- Academic Search Index
- Journal :
- New Astronomy
- Publication Type :
- Academic Journal
- Accession number :
- 155655327
- Full Text :
- https://doi.org/10.1016/j.newast.2021.101761