{"paper":{"title":"The semi-classical Maupertuis-Jacobi correspondence: 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":"2012-06-23T16:35:57Z","abstract_excerpt":"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 $h\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5409","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"}