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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Equivariant Morse theory for flows and an application to the $N$-body problem


Author: Filomena Pacella
Journal: Trans. Amer. Math. Soc. 297 (1986), 41-52
MSC: Primary 58F25; Secondary 58E05, 58F40, 70F10
DOI: https://doi.org/10.1090/S0002-9947-1986-0849465-9
MathSciNet review: 849465
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Abstract: In this paper, using Conley’s index and equivariant cohomology, some Morse type inequalities are deduced for a flow equivariant with respect to the action of a compact topological group. In the case of a gradient flow induced by a nondegenerate smooth function these inequalities coincide with those described by R. Bott. The theory is applied to the study of the central configurations of $N$-bodies.


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Keywords: Conley’s index, group actions, Morse inequalities, <IMG WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img5.gif" ALT="$N$">-body problem
Article copyright: © Copyright 1986 American Mathematical Society