{"paper":{"title":"Complex H\\'enon maps and discrete groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.GR"],"primary_cat":"math.DS","authors_text":"Raluca Tanase","submitted_at":"2015-03-12T10:53:08Z","abstract_excerpt":"Consider the standard family of complex H\\'enon maps $H(x,y) = (p(x) - ay, x)$, where $p$ is a quadratic polynomial and $a$ is a complex parameter. Let $U^{+}$ be the set of points that escape to infinity under forward iterations. The analytic structure of the escaping set $U^{+}$ is well understood from previous work of J. Hubbard and R. Oberste-Vorth as a quotient of $(\\mathbb{C}-\\overline{\\mathbb{D}}) \\times\\mathbb{C}$ by a discrete group of automorphisms $\\Gamma$ isomorphic to $\\mathbb{Z}[1/2]/\\mathbb{Z}$. On the other hand, the boundary $J^{+}$ of $U^{+}$ is a complicated fractal object o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03665","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"}