On certain M\"obius type solutions for the n-body problem in a positive space form

J. Guadalupe Reyes-Victoria; Pedro Pablo Ortega Palencia

On certain M\"obius type solutions for the n-body problem in a positive space form

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arxiv 1508.03209 v3 pith:2S2VM2VW submitted 2015-08-13 math.DS

Pedro Pablo Ortega Palencia , J. Guadalupe Reyes-Victoria This is my paper · ORCID

classification math.DS

keywords obiussolutionstypeformn-bodypositiveproblemspace

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We study here the Mobius type solutions for the n-body problem in a two dimensional positive space form M^2_R. With methods of Mobius geometry and using the Iwasawa decomposition of the Mobius group of automorphisms Mob_2 (M^2_R), we state algebraic functional conditions for the existence of such type of solutions in M^2_R. We mention some examples of these type of solutions.

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Conjugated equilibrium solutions for the $2$--body problem in the two dimensional sphere $\mathbb{M}^2_R$ for equal masses
physics.class-ph 2019-08 conditional novelty 4.0 of 10

Using a new cot(theta/2) potential, the authors show that antipodal configurations on the sphere arise as limits of isosceles relative equilibria and satisfy a regularized equation of motion.

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