{"paper":{"title":"Reducibility of 1-d Schroedinger equation with time quasiperiodic unbounded perturbations, I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dario Bambusi","submitted_at":"2016-06-14T18:41:34Z","abstract_excerpt":"We study the Schr\\\"odinger equation on $\\R$ with a polynomial potential behaving as $x^{2l}$ at infinity, $1\\leq l\\in\\N$ and with a small time quasiperiodic perturbation. We prove that if the symbol of the perturbation grows at most like $(\\xi^2+x^{2l})^{\\beta/(2l)}$, with $\\beta<l+1$, then the system is reducible. Some extensions including cases with $\\beta=2l$ are also proved. The result implies boundedness of Sobolev norms. The proof is based on pseudodifferential calculus and KAM theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04494","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"}