{"paper":{"title":"The semiclassical Maupertuis-Jacobi correspondence for quasi-periodic Hamiltonian flows: stable and unstable spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Michel Rouleux, Sergey Dobrokhotov","submitted_at":"2013-05-16T12:48:48Z","abstract_excerpt":"We investigate semi-classical properties of Maupertuis-Jacobi correspondence in 2-D for families of Hamiltonians $(H_\\lambda(x,\\xi), {\\cal H}_\\lambda(x,\\xi))$, when ${\\cal H}_\\lambda(x,\\xi)$ is the perturbation of completely integrable Hamiltonian $\\widetilde{\\cal H}$ veriying some isoenergetic non-degeneracy conditions. Assuming the Weyl $h$-PDO $H^w_\\lambda$ has only discrete spectrum near $E$, and the energy surface $\\{\\widetilde{\\cal H}={\\cal E}\\}$ is separated by some pairwise disjoint lagrangian tori, we show that most of eigenvalues for $\\hat H_\\lambda$ near $E$ are asymptotically degen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3785","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}