Abstract In the present manuscript, we unveil the topology of the basins of convergence in the regular polygon problem of ( N + 1 ) -bodies in two different cases, i.e., in case-I, only the central primary creates the Manev-type quasi-homogeneous potential, and in case-II, the peripheral primaries create the Manev-type quasi-homogeneous potential. The regular polygon problem of ( N + 1 ) -bodies describes the motion of the test particle moving in the force field of N primaries, the ν = N − 1 peripheral primaries of equal masses situated at the vertices of the imaginary regular ν − gon and the Nth primary with different mass i.e., the central primary situated at the centre of mass of the system. In this model, we assume that the primaries create quasi-homogeneous potentials instead of Newtonian potentials and forces. In order to approximate various phenomena due to the irregular shape of the primaries or due to emitting radiation, an inverse cube corrective term is inserted to the inverse square Newtonian law of gravitation. We, numerically, investigated the evolution of the positions of the libration points and their linear stability for different values of ν in both the cases. Further, the multivariate version of Newton-Raphson iterative scheme is applied to unveil the topology of the basins of convergence. Moreover, the ”basin entropy” is also computed to analyse the basins of convergence quantitatively.

中文翻译：

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(N+1)球体系统正多边形问题中收敛盆地的分析

摘要 在本手稿中，我们揭示了 ( N + 1 ) - 体的正多边形问题中收敛盆的拓扑结构，在两种不同情况下，即在情况 I 中，只有中心原色产生 Manev 型准-均质势，在情况 II 中，外围原色产生 Manev 型准均质势。( N + 1 ) -body 的正多边形问题描述了测试粒子在 N 个主力场中移动的运动，位于假想正则 ν - gon 顶点的 ν = N − 1 个质量相等的外围初级和具有不同质量的第 N 个初级，即位于系统质心的中央初级。在这个模型中，我们假设原色产生准齐次势而不是牛顿势和力。为了近似由于原色的不规则形状或由于发射辐射而引起的各种现象，在平方反比牛顿万有引力定律中插入了一个反立方校正项。我们从数值上研究了两种情况下振动点位置的演变及其对于不同 ν 值的线性稳定性。此外，牛顿-拉夫森迭代方案的多元版本被应用于揭示收敛盆地的拓扑结构。此外，还计算了“盆地熵”以定量分析收敛盆地。研究了两种情况下不同 ν 值的振动点位置的演变及其线性稳定性。此外，牛顿-拉夫森迭代方案的多元版本被应用于揭示收敛盆地的拓扑结构。此外，还计算了“盆地熵”以定量分析收敛盆地。研究了两种情况下不同 ν 值的振动点位置的演变及其线性稳定性。此外，牛顿-拉夫森迭代方案的多元版本被应用于揭示收敛盆地的拓扑结构。此外，还计算了“盆地熵”以定量分析收敛盆地。