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.References
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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