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On central congurations of the (kn)-body problem Barrabés Vera, Esther Cors Iglesias, Josep Maria Problema dels cossos múltiples Many-body problem Mecànica celest Celestial mechanics Òrbites Orbits We consider planar central configurations of the Newtonian kn-body problem consisting in k groups of regular n-gons of equal masses, called (k , n)-crown. We derive the equations of central configurations for a general ( k, n)-crown. When k = 2 we prove the existence of a twisted (2, n)-crown for any value of the mass ratio. Moreover, for n = 3, 4 and any value of the mass ratio, we give the exact number of twisted (2, n)-crowns, and describe their location. Finally, we conjecture that for any value of the mass ratio there exist exactly three (2; n)-crowns for n>=5 The authors are supported by MINECO grants MTM2016-80117-P and MTM2016-77278-P (FEDER) and Catalan (AGAUR) grants 2017 SGR 1374 and 2017 SGR 1617 2019-08-15 info:eu-repo/semantics/article info:eu-repo/semantics/submittedVersion peer-reviewed http://hdl.handle.net/10256/17086 http://hdl.handle.net/10256/17086 eng info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2019.04.010 info:eu-repo/semantics/altIdentifier/issn/0022-247X Tots els drets reservats info:eu-repo/semantics/openAccess 17 p. application/pdf Elsevier © Journal of Mathematical Analysis and Applications, 2019, vol. 476, núm. 2, p. 720-736 Articles publicats (D-IMAE) Barrabés Vera, Esther Cors Iglesias, Josep Maria 2019 On central congurations of the (kn)-body problem Journal of Mathematical Analysis and Applications 476 2 720 736