{"paper":{"title":"On parameter loci of the H\\'enon family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yutaka Ishii, Zin Arai","submitted_at":"2015-01-07T05:08:13Z","abstract_excerpt":"The purpose of the current article is to investigate the dynamics of the H\\'enon family $f_{a, b} : (x, y) \\mapsto (x^2-a-by, x)$, where $(a, b)\\in \\mathbb{R}\\times\\mathbb{R}^{\\times}$ is the parameter~\\cite{H}. We are interested in certain geometric and topological structures of two loci of parameters $(a, b)\\in\\mathbb{R}\\times\\mathbb{R}^{\\times}$ for which $f_{a, b}$ share common dynamical properties; one is the \\textit{hyperbolic horseshoe locus} where the restriction of $f_{a, b}$ to its non-wandering set is hyperbolic and topologically conjugate to the full shift with two symbols, and the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01368","kind":"arxiv","version":4},"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"}