{"paper":{"title":"On parametric Gevrey asymptotics for some Cauchy problems in quasiperiodic function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AP","authors_text":"Alberto Lastra, St\\'ephane Malek","submitted_at":"2014-03-18T18:39:04Z","abstract_excerpt":"We investigate Gevrey asymptotics for solutions to nonlinear parameter depending Cauchy problems with $2\\pi$-periodic coefficients, for initial data living in a space of quasiperiodic functions. By means of the Borel-Laplace summation procedure, we construct sectorial holomorphic solutions which are shown to share the same formal power series as asymptotic expansion in the perturbation parameter. We observe a small divisor phenomenon which emerges from the quasiperiodic nature of the solutions space and which is the origin of the Gevrey type divergence of this formal series. Our result rests o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4566","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"}