2012 | OriginalPaper | Chapter
Qualitative Behavior
Author : Florin Diacu
Published in: Relative Equilibria of the Curved N-Body Problem
Publisher: Atlantis Press
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In this chapter we will describe some qualitative dynamical properties for the positive elliptic, positive elliptic-elliptic, negative elliptic, negative hyperbolic, and negative elliptic-hyperbolic RE, under the assumption that they exist. (Examples of such solutions will be given in Part IV for various values of
N
and of the masses
$$ {\text{m}}_{ 1} , {\text{m}}_{ 2} ,\ldots , {\text{m}}_{\text{N}} { > 0} . $$
) For this purpose we will also provide some geometric-topologic considerations about
$$ {\text{S}}_{ 3} $$
and
$$ {\text{H}}_{ 3} $$
.