{"paper":{"title":"Melnikov theory to all orders and Puiseux series for subharmonic solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Guido Gentile, Livia Corsi","submitted_at":"2008-07-02T09:59:47Z","abstract_excerpt":"We study the problem of subharmonic bifurcations for analytic systems in the plane with perturbations depending periodically on time, in the case in which we only assume that the subharmonic Melnikov function has at least one zero. If the order of zero is odd, then there is always at least one subharmonic solution, whereas if the order is even in general other conditions have to be assumed to guarantee the existence of subharmonic solutions. Even when such solutions exist, in general they are not analytic in the perturbation parameter. We show that they are analytic in a fractional power of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0314","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"}