Equivariant Morse theory for flows and an application to the -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 -bodies.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0849465-9

Keywords:
Conley's index,
group actions,
Morse inequalities,
-body problem

Article copyright:
© Copyright 1986
American Mathematical Society