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首页> 外文期刊>International journal of non-linear mechanics >Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential
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Fractal basins of convergence of libration points in the planar Copenhagen problem with a repulsive quasi-homogeneous Manev-type potential

机译：具有排斥半准Manev型势的平面哥本哈根问题中解放点收敛的分形盆地

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摘要

The Newton Raphson basins of convergence, corresponding to the coplanar libration points (which act as attractors), are unveiled in the Copenhagen problem, where instead of the Newtonian potential and forces, a quasi-homogeneous potential created by two primaries is considered. The multivariate version of the Newton Raphson iterative scheme is used to reveal the attracting domain associated with the libration points on various type of two-dimensional configuration planes. The correlations between the basins of convergence and the corresponding required number of iterations are also presented and discussed in detail. The present numerical analysis reveals that the evolution of the attracting domains in this dynamical system is very complicated, however, it is a worth studying issue.
机译：在哥本哈根问题中揭示了与共面解放点（充当吸引子）相对应的牛顿拉弗森收敛盆地，其中考虑了由两个原初产生的准均质势而不是牛顿势和力。牛顿拉夫森迭代方案的多元版本用于揭示与各种类型的二维配置平面上的释放点相关的吸引域。还详细介绍并讨论了收敛盆地和相应的所需迭代次数之间的相关性。目前的数值分析表明，该动力系统中吸引域的演化非常复杂，但这是一个值得研究的问题。

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