2015
DOI: 10.1007/s12346-015-0170-z
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Open Problem 1: Are Palmore’s “Ignored Estimates” on the Number of Planar Central Configurations Correct?

Abstract: Abstract. We wish to draw attention on estimates on the number of relative equilibria in the Newtonian n-body problem that Julian Palmore published in 1975.Julian Palmore published in [12] a first estimate on the number of planar central configurations with given number of bodies n and given positive masses m 1 , . . . , m n . If these central configurations are non-degenerate, they are at least (3n − 4)(n − 1)!/2.The word "configuration" is ambiguous. Here we consider two "configurations" which are deduced on… Show more

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Cited by 5 publications
(2 citation statements)
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“…Another easy consequence of Lemma 4.1 is the following proposition (see [1,11,17] for its importance in estimating the number non-degenerate planar central configurations of four bodies). Proof .…”
Section: Simple Proofs Of Some Corollariesmentioning
confidence: 98%
“…Another easy consequence of Lemma 4.1 is the following proposition (see [1,11,17] for its importance in estimating the number non-degenerate planar central configurations of four bodies). Proof .…”
Section: Simple Proofs Of Some Corollariesmentioning
confidence: 98%
“…, n. For α = 1, it is the Newtonian gravitational interaction. There have been an active line of research on central configurations since decades: see for example [17], [4] [22]), [23], [15], [12], [2], [16], [1]. The purpose of this article is to survey some recent results (mostly of the author) in this field, with applications of fixed point theory.…”
Section: Introductionmentioning
confidence: 99%