{"paper":{"title":"Birth of limit cycles for a class of continuous and discontinuous differential systems in (d+2)-dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"I.O. Zeli, J. Llibre, M.A. Teixeira","submitted_at":"2015-01-08T21:23:22Z","abstract_excerpt":"The orbits of the reversible differential system $\\dot{x}=-y$, $\\dot{y}=x$, $\\dot{z}=0$, with $x,y \\in R$ and $z\\in R^d$, are periodic with the exception of the equilibrium points $(0,0, z)$. We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system $\\dot{x}=-y$, $\\dot{y}=x$, $\\dot{z}=0$, using the averaging theory of first order, when this system is perturbed, first inside the class of all polynomial differential systems of degree $n$, and second inside the class of all discontinuous piecewise polynomial differential systems of degree $n$ with two pi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01987","kind":"arxiv","version":2},"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"}