{"paper":{"title":"Non-autonomous Parabolic Bifurcation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Liz Vivas","submitted_at":"2019-05-02T19:17:07Z","abstract_excerpt":"Let $f(z) = z+z^2+O(z^3)$ and $f_\\epsilon(z) = f(z) + \\epsilon^2$. A classical result in parabolic bifurcation in one complex variable is the following: if $N-\\frac{\\pi}{\\epsilon}\\to 0$ we obtain $(f_\\epsilon)^{N} \\to \\mathcal{L}_f$, where $\\mathcal{L}_f$ is the Lavaurs map of $f$. In this paper we study a \\textit{non-autonomous} parabolic bifurcation. We focus on the case of $f_0(z)=\\frac{z}{1-z}$. Given a sequence $\\{\\epsilon_i\\}_{1\\leq i\\leq N}$, we denote $f_n(z) = f_0(z) + \\epsilon_n^2$. We give sufficient and necessary conditions on the sequence $\\{\\epsilon_i\\}$ that imply that $f_{N}\\ci"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.00937","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"}