{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AAC7WP5EJSQG53U6LR3Q7UUNZH","short_pith_number":"pith:AAC7WP5E","schema_version":"1.0","canonical_sha256":"0005fb3fa44ca06eee9e5c770fd28dc9fcf6f28f4afafe055832b1207c635dc6","source":{"kind":"arxiv","id":"1401.3593","version":1},"attestation_state":"computed","paper":{"title":"Examples of nearly integrable systems on $\\mathbb{A}^3$ with asymptotically dense projected orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Jean-Pierre Marco, Lara Sabbagh","submitted_at":"2014-01-15T14:02:34Z","abstract_excerpt":"Given an integer $\\kappa\\geq2$, we introduce a class of nearly integrable systems on $\\mathbb{A}^3$, of the form $$ H_n(\\theta,r)=\\frac12 \\Vert r\\Vert ^2+\\tfrac{1}{n} U(\\theta_2,\\theta_3)+f_n(\\theta,r) $$ where $U\\in C^\\kappa(\\mathbb{T}^2)$ is a generic potential function and $f_n$ a $C^{\\kappa-1}$ additional perturbation such that $\\Vert f_n\\Vert_{C^{\\kappa-1}(\\mathbb{A}^3)}\\leq \\tfrac{1}{n}$, so that $H_n$ is a perturbation of the completely integrable system $h(r)=\\frac12\\Vert r\\Vert ^2$.\n  Let $\\Pi:\\mathbb{A}^3\\to\\mathbb{R}^3$ be the canonical projection. We prove that for each $\\delta>0$,"},"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":"1401.3593","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-01-15T14:02:34Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"04d9b1287b6de8029fed97430faffaaa44fac9158fe03e581fc2a6c43920f3ed","abstract_canon_sha256":"702ff4ee18d989745b78d70db503e18d4511fbc1bf2e6ad5b62f5caa3093f64e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:08.276814Z","signature_b64":"5PT6X7NlpDkjxJyKDMiJGouMgeWJVAY8Cw71xFkDvqTXDOSAnJmWxTnYTmE5LMWCD3Ac8IPyDm6m7/XWMKOWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0005fb3fa44ca06eee9e5c770fd28dc9fcf6f28f4afafe055832b1207c635dc6","last_reissued_at":"2026-05-18T03:02:08.276012Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:08.276012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Examples of nearly integrable systems on $\\mathbb{A}^3$ with asymptotically dense projected orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Jean-Pierre Marco, Lara Sabbagh","submitted_at":"2014-01-15T14:02:34Z","abstract_excerpt":"Given an integer $\\kappa\\geq2$, we introduce a class of nearly integrable systems on $\\mathbb{A}^3$, of the form $$ H_n(\\theta,r)=\\frac12 \\Vert r\\Vert ^2+\\tfrac{1}{n} U(\\theta_2,\\theta_3)+f_n(\\theta,r) $$ where $U\\in C^\\kappa(\\mathbb{T}^2)$ is a generic potential function and $f_n$ a $C^{\\kappa-1}$ additional perturbation such that $\\Vert f_n\\Vert_{C^{\\kappa-1}(\\mathbb{A}^3)}\\leq \\tfrac{1}{n}$, so that $H_n$ is a perturbation of the completely integrable system $h(r)=\\frac12\\Vert r\\Vert ^2$.\n  Let $\\Pi:\\mathbb{A}^3\\to\\mathbb{R}^3$ be the canonical projection. 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