arXiv subjects
Publications and source records attributed to Pedro Pablo Ortega Palencia.
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.
By using, the Vlasov-Poisson equation defined in either a Riemannian or a semi-Riemannian space $\mathbb{R}^k_g$, and a Dirac distribution function, we re-obtain the well known and classical equations of motion of a mechanical system with a pairwise acting potential function. We apply this result to the study of an $n$--body problem in a two dimensional negative space form with the hyperbolic cotangent potential. Following the Klein's geometric Erlangen program, with methods of Möbius geometry and using the Iwasawa decomposition of the Möbius isometric group $SL(2,\mathbb{R})$ via its representation in one Clifford Algebra, we complete the study of the whole set of Möbius solutions (relative equilibria) of the problem begun by Diacu {\it et al.} in \cite{Diacu8}.