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

Pacella, Filomena

doi:10.1090/S0002-9947-1986-0849465-9

Equivariant Morse theory for flows and an application to the $N$-body problem
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Trans. Amer. Math. Soc. 297 (1986), 41-52 Request permission

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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