On certain M\"obius type solutions for the n-body problem in a positive space form
Pedro Pablo Ortega Palencia, J. Guadalupe Reyes-Victoria
TL;DR
This paper investigates M"obius type solutions for the n-body problem in a two-dimensional positive space form, using M"obius geometry and algebraic conditions to identify such solutions and providing examples.
Contribution
It introduces algebraic functional conditions for M"obius type solutions in M^2_R and demonstrates their existence with specific examples.
Findings
Derived algebraic conditions for M"obius solutions
Identified examples of such solutions in M^2_R
Applied M"obius geometry and Iwasawa decomposition methods
Abstract
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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Taxonomy
TopicsAdvanced Differential Geometry Research · Advanced Differential Equations and Dynamical Systems · Spacecraft Dynamics and Control