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Proceedings of the American Mathematical Society

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

 

 

The second Birkhoff theorem for optical Hamiltonian systems


Author: Leonid Polterovich
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1991-1043418-3
Article copyright: © Copyright 1991 American Mathematical Society