1976
DOI: 10.2307/1970964
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Measure of Degenerate Relative Equilibria. I

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Cited by 50 publications
(27 citation statements)
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“…Palmore [10]), so the critical set may possibly be infinite. In fact, it is either finite or contains a continuum (cf.…”
Section: Old and Recent Results On Central Configurations (For The Grmentioning
confidence: 99%
“…Palmore [10]), so the critical set may possibly be infinite. In fact, it is either finite or contains a continuum (cf.…”
Section: Old and Recent Results On Central Configurations (For The Grmentioning
confidence: 99%
“…By a theorem [3] on the existence of degeneracies of Vm for some (mi) E IR~ and for any n > 4 the minimal classification is not always realized. For any three positive masses ~',n is always a Morse function so that in this case the lower bound is always realized.…”
Section: Forany N >3 and Forany K >0mentioning
confidence: 99%
“…We refer to previous results [3] on the existence of degeneracies of Vm for some (mi)E IR n and for any n > 4. Here there is a one parameter family of relative equilibria classes along which an index change occurs from maximum (index = 2n -4) to saddle (index -2n -6) at a unique ratio of the masses.…”
Section: I N I M a L C L A S S I F I C A T I O N Smentioning
confidence: 99%
“…if U is a Morse function. Palmore has shown that this is not always true [17]. The set of masses for which he can give examples of degenerate critical points is of codimension one in the set of all masses.…”
mentioning
confidence: 99%
“…The set of masses for which he can give examples of degenerate critical points is of codimension one in the set of all masses. Palmore has also announced that the set of masses which admit degenerate critical points has measure zero in the set of all masses [17]; however, no proof has appeared. Much of the work described above deals with the problem of determining for each fixed m the corresponding relative equilibria.…”
mentioning
confidence: 99%