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- W2001049957 abstract "We investigate semi-classical properties of Maupertuis-Jacobi correspondence for families of 2-D Hamiltonians $(H_lambda(x,xi), {cal H}_lambda(x,xi))$, when ${cal H}_lambda(x,xi)$ is the perturbation of a completely integrable Hamiltonian $widetilde{cal H}$ veriying some isoenergetic non-degeneracy conditions. Assuming $hat H_lambda$ has only discrete spectrum near $E$, and the energy surface ${widetilde{cal H}_0={cal E}}$ is separated by some pairwise disjoint Lagrangian tori, we show that most of eigenvalues for $hat H_lambda$ near $E$ are asymptotically degenerate as $hto0$. This applies in particular for the determination of trapped modes by an island, in the linear theory of water-waves. We also consider quasi-modes localized near rational tori. Finally, we discuss breaking of Maupertuis-Jacobi correspondence on the equator of Katok sphere." @default.
- W2001049957 created "2016-06-24" @default.
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- W2001049957 date "2012-06-23" @default.
- W2001049957 modified "2023-09-27" @default.
- W2001049957 title "The semi-classical Maupertuis-Jacobi correspondence: stable and unstable spectra" @default.
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