arXiv 0801.48822008-01math-phmath.MP

The Semi Classical Maupertuis-Jacobi Correspondance for Quasi-Periodic Hamiltonian Flows

Sergey Dobrokhotov, Michel Rouleux

备注：: ~40 pages

英文摘要：

We extend to the semi-classical setting the Maupertuis-Jacobi correspondance for a pair of hamiltonians $(H(x,hD_x), {\cal H}(x,hD_x)$. If ${\cal H}(p,x)$ is completely integrable, or has merely has invariant diohantine torus $Λ$ in energy surface ${\cal E}$, then we can construct a family of quasi-modes for $H(x,hD_x)$ at the corresponding energy $E$. This applies in particular to the theory of water-waves in shallow water, and determines trapped modes by an island, from the knowledge of Liouville metrics.

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