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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The second Birkhoff theorem for optical Hamiltonian systems
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by Leonid Polterovich PDF
Proc. Amer. Math. Soc. 113 (1991), 513-516 Request permission

Abstract:

Consider a smooth Hamiltonian function on the cotangent bundle of the $n$-dimensional torus such that its restriction on every fiber is strictly convex. Let $L$ be a Lagrange invariant torus of the Hamiltonian flow which is homologous to the zero section. We show that, under some assumptions, $L$ is a smooth section of the cotangent bundle.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 513-516
  • MSC: Primary 58F05; Secondary 53C22, 58F17
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1043418-3
  • MathSciNet review: 1043418