Revealing the basins of convergence in the planar equilateral restricted four-body problem

  • Euaggelos E. Zotos
Original Article


The planar equilateral restricted four-body problem where two of the primaries have equal masses is used in order to determine the Newton-Raphson basins of convergence associated with the equilibrium points. The parametric variation of the position of the libration points is monitored when the value of the mass parameter \(m_{3}\) varies in predefined intervals. The regions on the configuration \((x,y)\) plane occupied by the basins of attraction are revealed using the multivariate version of the Newton-Raphson iterative scheme. The correlations between the attracting domains of the equilibrium points and the corresponding number of iterations needed for obtaining the desired accuracy are also illustrated. We perform a thorough and systematic numerical investigation by demonstrating how the dynamical parameter \(m_{3}\) influences the shape, the geometry and the degree of fractality of the converging regions. Our numerical outcomes strongly indicate that the mass parameter is indeed one of the most influential factors in this dynamical system.


Restricted four body-problem Equilibrium points Basins of attraction Fractal basins boundaries 



I would like to express my warmest thanks to the anonymous referee for the careful reading of the manuscript and for all the apt suggestions and comments which allowed us to improve both the quality and the clarity of the paper.


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Physics, School of ScienceAristotle University of ThessalonikiThessalonikiGreece

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