{"paper":{"title":"Limit cycles appearing from perturbations of cubic piecewise smooth center with double invariant real straight lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jihua Yang, Liqin Zhao","submitted_at":"2018-08-05T02:30:55Z","abstract_excerpt":"This paper investigates the exact number of limit cycles given by the averaging theory of first order for the piecewise smooth integrable non-Hamiltonian system \\begin{eqnarray*} (\\dot{x},\\ \\dot{y})=\\begin{cases} (-y(x+a)^2+\\varepsilon f^+(x,y),\\ x(x+a)^2+\\varepsilon g^+(x,y)),\\ \\ x\\geq0,\\\\ (-y(x+b)^2+\\varepsilon f^-(x,y),\\ x(x+b)^2+\\varepsilon g^-(x,y)),\\ ~ \\, x<0,\\\\ \\end{cases}\\end{eqnarray*} where $ab\\neq 0$, $0<|\\varepsilon|\\ll 1$, and $f^\\pm(x,y)$ and $g^\\pm(x,y)$ are polynomials of degree $n$. It is proved that the exact number of limit cycles emerging from the period annulus surrounding"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01553","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"}