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<p>In this work, we consider the existence of (3,&#xa0;<i>n</i>)–crowns in the classical Newtonian 3<i>n</i>–body problem, which are central configurations formed by three groups of <i>n</i> bodies with the same mass within each group, located at the vertices of three concentric regular polygons. We consider the case with dihedral symmetry, called nested (3,&#xa0;<i>n</i>)–crowns, where the vertices of the polygons are aligned. We characterize the set of admissible radii for the polygons for which nested (3,&#xa0;<i>n</i>)–crowns exist. We conclude with numerical evidences that suggest uniqueness for each set of three masses.</p>

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On Nested Central Configurations of the 3n Body Problem

  • 期刊论文

  • 发表日期：

    2025年5月2日

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  • E. Barrabés,
  • J. M. Cors,
  • A. C. Fernandes,
  • C. Vidal

摘要

In this work, we consider the existence of (3, n)–crowns in the classical Newtonian 3n–body problem, which are central configurations formed by three groups of n bodies with the same mass within each group, located at the vertices of three concentric regular polygons. We consider the case with dihedral symmetry, called nested (3, n)–crowns, where the vertices of the polygons are aligned. We characterize the set of admissible radii for the polygons for which nested (3, n)–crowns exist. We conclude with numerical evidences that suggest uniqueness for each set of three masses.