Abstract
In this chapter we will introduce the concept of fixed-point solution, also simply called fixed point (from now on denoted by FP, whether in the singular or the plural form of the noun) of the equations of motion, show that FP exist in \( {\text{S}}^{ 3} \), provide a couple of examples, and finally prove that they don’t show up in \( {\text{H}}^{ 3} \) and in hemispheres of \( {\text{S}}^{ 3} \), provided that at least one body is not on the boundary of the hemisphere.
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© 2012 Florin Diacu
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Diacu, F. (2012). Fixed Points (FP). In: Relative Equilibria of the Curved N-Body Problem. Atlantis Series in Dynamical Systems, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-91216-68-8_6
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DOI: https://doi.org/10.2991/978-94-91216-68-8_6
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Publisher Name: Atlantis Press, Paris
Print ISBN: 978-94-91216-67-1
Online ISBN: 978-94-91216-68-8
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