{"paper":{"title":"A structure theorem for semi-parabolic H\\'enon maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Raluca Tanase, Remus Radu","submitted_at":"2014-11-14T08:28:13Z","abstract_excerpt":"Consider the parameter space $\\mathcal{P}_{\\lambda}\\subset \\mathbb{C}^{2}$ of complex H\\'enon maps $$ H_{c,a}(x,y)=(x^{2}+c+ay,ax),\\ \\ a\\neq 0 $$ which have a semi-parabolic fixed point with one eigenvalue $\\lambda=e^{2\\pi i p/q}$. We give a characterization of those H\\'enon maps from the curve $\\mathcal{P}_{\\lambda}$ that are small perturbations of a quadratic polynomial $p$ with a parabolic fixed point of multiplier $\\lambda$. We prove that there is an open disk of parameters in $\\mathcal{P}_{\\lambda}$ for which the semi-parabolic H\\'enon map has connected Julia set $J$ and is structurally s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3824","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"}