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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Equivariant Morse theory for starshaped Hamiltonian systems


Author: Claude Viterbo
Journal: Trans. Amer. Math. Soc. 311 (1989), 621-655
MSC: Primary 58F05; Secondary 58E05, 58F35
MathSciNet review: 978370
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Abstract: Let $ \Sigma $ be a starshaped hypersurface in $ {R^{2n}}$; the problem of finding closed characteristics of $ \Sigma $ can be classically reduced to a variational problem. This leads to studying an $ {S^1}$-equivariant functional on a Hilbert space. The equivariant Morse theory of this functional, together with the assumption that $ \Sigma $ only has finitely many geometrically distinct characteristics, leads to a remarkable formula relating the average indices of the characteristics. Using this formula one can prove, at least for $ n$ even, that genetically there are infinitely many characteristics (cf. [E1] for the convex case).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0978370-5
PII: S 0002-9947(1989)0978370-5
Keywords: Hamiltonian systems, closed characteristics, periodic orbits
Article copyright: © Copyright 1989 American Mathematical Society