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On the Convergence Dynamics of the Sitnikov Problem with Non-spherical Primaries

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Abstract

We investigate, using numerical methods, the convergence dynamics of the Sitnikov problem with non-spherical primaries, by applying the Newton–Raphson iterative scheme. In particular, we examine how the oblateness parameter A influences several aspects of the method, such as its speed and efficiency. Color-coded diagrams are used for revealing the convergence basins on the plane of complex numbers. Moreover, we compute the degree of fractality of the convergence basins on the complex space, as a relation of the oblateness, by using different computational tools, such the fractal dimension as well as the (boundary) basin entropy.

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Authors and Affiliations

  1. Department of Physics, School of Science, Aristotle University of Thessaloniki, 541 24, Thessaloniki, Greece

    Euaggelos E. Zotos

  2. Department of Mathematics, Sri Aurobindo College, University of Delhi, New Delhi, 110017, India

    Md Sanam Suraj

  3. Department of Mathematics, Deshbandhu College, University of Delhi, New Delhi, 110019, India

    Rajiv Aggarwal

  4. Department of Mathematics, ARSD College, University of Delhi, New Delhi, 110021, India

    Amit Mittal

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  1. Euaggelos E. Zotos
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  2. Md Sanam Suraj
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  3. Rajiv Aggarwal
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Correspondence to Euaggelos E. Zotos.

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Zotos, E.E., Suraj, M.S., Aggarwal, R. et al. On the Convergence Dynamics of the Sitnikov Problem with Non-spherical Primaries. Int. J. Appl. Comput. Math 5, 43 (2019). https://doi.org/10.1007/s40819-019-0627-x

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