{"paper":{"title":"Hyperbolicity and Averaging for the Srzednicki-W\\'ojcik equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Piotr Zgliczy\\'nski","submitted_at":"2016-07-09T13:26:19Z","abstract_excerpt":"For the Srzednicki-W\\'ojcik equation, the planar nonautonomous ODE parameterized by $\\kappa \\in \\mathbb{R}$,  $$ z'=\\overline{z}(1+ |z|^2 \\exp(i \\kappa t)), \\qquad z(t) \\in \\mathbb{C} $$ using averaging we show how the region of hyperbolicty grows with $|\\kappa|$. Based on this we give bounds on the sizes of bounded orbits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.02611","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"}