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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.01368","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-07T05:08:13Z","cross_cats_sorted":[],"title_canon_sha256":"d3cbe092240544b68865a153e91bebac2e929b81ebaf0386b937f08d3df80328","abstract_canon_sha256":"4fd602aee8ff7219bf51a12697ac31b687639a85ec78a0a4e514894455ec8e1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:49.543288Z","signature_b64":"cCJ4vht0CwrxQof6PENUxfs8E/9/E/KMQAz7GrimgUejSLtLsxK1THQ3PxTthVtqwuLdYBWQ/KNsY7jApyHCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8721c043d8c78e0a5dfc8d01c520b693ed7f5083a2f5a0b0451dc08722d0697d","last_reissued_at":"2026-05-18T00:20:49.542762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:49.542762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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}. 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