The second Birkhoff theorem for optical Hamiltonian systems
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 by Leonid Polterovich PDF
 Proc. Amer. Math. Soc. 113 (1991), 513516 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.References

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Additional Information
 © Copyright 1991 American Mathematical Society
 Journal: Proc. Amer. Math. Soc. 113 (1991), 513516
 MSC: Primary 58F05; Secondary 53C22, 58F17
 DOI: https://doi.org/10.1090/S00029939199110434183
 MathSciNet review: 1043418