{"paper":{"title":"Isochronicity conditions for some planar polynomial systems II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"A. Raouf Chouikha, Islam Boussaada, Jean-Marie Strelcyn, Magali Bardet","submitted_at":"2010-05-27T12:36:31Z","abstract_excerpt":"We study the isochronicity of centers at $O\\in \\mathbb{R}^2$ for systems $$\\dot x=-y+A(x,y),\\;\\dot y=x+B(x,y),$$ where $A,\\;B\\in \\mathbb{R}[x,y]$, which can be reduced to the Li\\'enard type equation. When $deg(A)\\leq 4$ and $deg(B) \\leq 4$, using the so-called C-algorithm we found $36$ new families of isochronous centers. When the Urabe function $h=0$ we provide an explicit general formula for linearization. This paper is a direct continuation of \\cite{BoussaadaChouikhaStrelcyn2010} but can be read independantly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5048","kind":"arxiv","version":4},"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"}