{"paper":{"title":"Generalized H\\'enon mappings and foliation by injective Brody curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Taeyong Ahn","submitted_at":"2014-10-24T05:31:47Z","abstract_excerpt":"We consider a finite composition of generalized H\\'{e}non mappings $\\mathfrak{f}:\\mathbb{C}^2\\to\\mathbb{C}^2$ and its Green function $\\mathfrak{g}^+:\\mathbb{C}^2\\to\\mathbb{R}_{\\ge 0}$ (see Section 2). It is well known that each level set $\\{\\mathfrak{g}^+=c\\}$ for $c>0$ is foliated by biholomorphic images of $\\mathbb{C}$ and each leaf is dense. In this paper, we prove that each leaf is actually an injective Brody curve in $\\mathbb{P}^2$ (see Section 4). Namely, for any injective holomorphic parametrization of any leaf, its derivative is bounded over $\\mathbb{C}$ with respect to the Fubini-Stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6576","kind":"arxiv","version":3},"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"}