{"paper":{"title":"Cubic perturbations of elliptic Hamiltonian vector fields of degree three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Iliya D. Iliev, Lubomir Gavrilov","submitted_at":"2014-06-01T21:26:37Z","abstract_excerpt":"The purpose of the present paper is to study the limit cycles of one-parameter perturbed plane Hamiltonian vector field $X_\\varepsilon$ $$ X_\\varepsilon : \\left\\{ \\begin{array}{llr} \\dot{x}=\\;\\; H_y+\\varepsilon f(x,y)\\\\ \\dot{y}=-H_x+\\varepsilon g(x,y), \\end{array} \\;\\;\\;\\;\\; H~=\\frac{1}{2} y^2~+U(x)\n  \\right. $$ which bifurcate from the period annuli of $X_0$ for sufficiently small $\\varepsilon$. Here $U$ is a univariate polynomial of degree four without symmetry, and $f, g$ are arbitrary cubic polynomials in two variables.\n  We take a period annulus and parameterize the related displacement m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0208","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"}