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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Equivariant Morse theory for starshaped Hamiltonian systems
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by Claude Viterbo PDF
Trans. Amer. Math. Soc. 311 (1989), 621-655 Request permission

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
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 311 (1989), 621-655
  • MSC: Primary 58F05; Secondary 58E05, 58F35
  • DOI: https://doi.org/10.1090/S0002-9947-1989-0978370-5
  • MathSciNet review: 978370