{"paper":{"title":"Bifurcation of critical periods from Pleshkan's isochrones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jordi Villadelprat, Maite Grau","submitted_at":"2008-11-14T11:17:56Z","abstract_excerpt":"Pleshkan proved in 1969 that, up to a linear transformation and a constant rescaling of time, there are four isochrones in the family of cubic centers with homogeneous nonlinearities $\\mathscr C_3.$ In this paper we prove that if we perturb any of these isochrones inside $\\mathscr C_3,$ then at most two critical periods bifurcate from its period annulus. Moreover we show that, for each $k=0,1,2,$ there are perturbations giving rise to exactly $k$ critical periods. As a byproduct, we obtain a partial result for the analogous problem in the family of quadratic centers $\\mathscr C_2.$ Loud proved"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.2317","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"}