{"paper":{"title":"Singular perturbation of nonlinear systems with regular singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Domingos H. U. Marchetti, William R. P. Conti","submitted_at":"2012-07-17T20:26:08Z","abstract_excerpt":"We extend Balser-Kostov method of studying summability properties of a singularly perturbed inhomogeneous linear system with regular singularity at origin to nonlinear systems of the form \\varepsilon zf^{\\prime} = F(\\varepsilon,z,f) with F a \\mathbb{C}^{\\nu}-valued function, holomorphic in a polydisc \\bar{D}_{\\rho}\\times \\bar{D}_{\\rho}\\times \\bar{D}_{\\rho}^{\\nu}. We show that its unique formal solution in power series of \\varepsilon, whose coefficients are holomorphic functions of z, is 1-summable under a Siegal-type condition on the eigenvalues of F_{f}(0,0,0). The estimates employed resemble"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4212","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"}