{"paper":{"title":"Uniform upper bounds for the cyclicity of the zero solution of the Abel differential equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Dmitry Batenkov, Gal Binyamini","submitted_at":"2015-04-09T07:31:24Z","abstract_excerpt":"Given two polynomials $P,q$ we consider the following question: \"how large can the index of the first non-zero moment $\\tilde{m}_k=\\int_a^b P^k q$ be, assuming the sequence is not identically zero?\". The answer $K$ to this question is known as the moment Bautin index, and we provide the first general upper bound: $K\\leqslant 2+\\mathrm{deg} q+3(\\mathrm{deg} P-1)^2$. The proof is based on qualitative analysis of linear ODEs, applied to Cauchy-type integrals of certain algebraic functions.\n  The moment Bautin index plays an important role in the study of bifurcations of periodic solution in the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02208","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"}