{"paper":{"title":"Semi-classical resonances associated with a periodic orbit of hyperbolic type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Hanen Louati, Michel Rouleux","submitted_at":"2016-06-20T15:39:34Z","abstract_excerpt":"We consider in this Note resonances for a $h$-Pseudo-Differential Operator $H(x,hD_x;h)$ on $L^2(M)$ induced by a periodic orbit of hyperbolic type, as arises for Schr\\\"odinger operator with AC Stark effect when $M={\\bf R}^n$, or the geodesic flow on an axially symmetric manifold $M$, extending Poincar\\'e example of Lagrangian systems with 2 degrees of freedom. We generalize the framework of [G\\'eSj], in the sense that we allow for hyperbolic and elliptic eigenvalues of Poincar\\'e map, and look for so-called semi-excited resonances with imaginary part of magnitude $-h\\log h$, or $h^s$, with $0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06180","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"}