Abstract
Consider an initial Lagrangian submanifold Λ0 ⊂ T* ℝn that admits a global generating function and a Hamiltonian isotopy Φ t H . Then, we provide a global generating function for the Lagrangian submanifold Λ t = Φ t H (Λ0) realized by applying the so-called Amann-Conley-Zehnder reduction. When Λ0 is the zero-section, we study in some detail the asymptotic behavior of such generating functions and give an approximation result.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 33, Suzdal Conference-2004, Part 1, 2005.
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Bettiol, P. Some properties of generating functions obtained by Amann-Conley-Zehnder reduction. J Math Sci 144, 3760–3774 (2007). https://doi.org/10.1007/s10958-007-0229-8
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DOI: https://doi.org/10.1007/s10958-007-0229-8