 98554 Gareth E. Roberts
 A Continuum of Relative Equilibria in the 5Body Problem
(18K, LATeX 2e)
Aug 6, 98

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Abstract. It is generally believed that the set of relative
equilibria equivalence classes in the Newtonian $n$body problem,
for a given set of positive masses, is finite.
However, the result
has only been proven for $n=3$ and remains a difficult, open
question for $n \geq 4$ (Wintner~\cite{cc:wint}, Smale~\cite{cc:smale1}).
We demonstrate that the condition
for the masses being positive is a necessary one by finding a
continuum of relative equilibria in the fivebody problem which (unfortunately)
includes one negative mass. This family persists in similar
potential functions,
including the logarithmic potential used to describe
the motion of point vortices in a plane of fluid.
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