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Consider a real-analytic nearly-integrable mechanical system with potential $f$, namely, a Hamiltonian system with real-analytic Hamiltonian $$H(y,x)=\\frac12 \\sum_{i=1}^n y_i^2 +\\epsilon f(x)\\ ,$$ $(y,x)\\in{\\mathbb R}^n\\times{\\mathbb T}^n$ being standard action--angle variables. For \"general non-degenerate\" potentials $f$'s there exists $\\epsilon_0,a>0$ such that, if $0<\\epsilon<\\epsilon_0$, then the Liouville measure of the complementary of $H$-invariant to"},"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":"1702.06480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-21T17:22:02Z","cross_cats_sorted":[],"title_canon_sha256":"0f73bc8ef7cf18816e80c11d74a52d481740f61fde8829110f4d09f59a03856e","abstract_canon_sha256":"1461c18e44f89d2a2481c7c35889f3160801cb7d848e7bceb40d9f9ca5f4b91f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:14.026923Z","signature_b64":"10XTLsADwh3DE7eoC8MxuXzG72s3c/BVxybCUudtMs+/Bve4vvAJNeysHdtrHYP6dJFNKcXk9V03vXATzHemDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17c51b125848f8c5c1054910d207b80e94808ad9083f9e8a5fdf14b6df722de4","last_reissued_at":"2026-05-18T00:50:14.026527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:14.026527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"KAM Theory for secondary tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Luca Biasco, Luigi Chierchia","submitted_at":"2017-02-21T17:22:02Z","abstract_excerpt":"In [3] (Rend. Lincei Mat. Appl. 26 (2015), 1-10; see also arXiv:1503.08145 [math.DS]) the following result has been announced:\n  Theorem. Consider a real-analytic nearly-integrable mechanical system with potential $f$, namely, a Hamiltonian system with real-analytic Hamiltonian $$H(y,x)=\\frac12 \\sum_{i=1}^n y_i^2 +\\epsilon f(x)\\ ,$$ $(y,x)\\in{\\mathbb R}^n\\times{\\mathbb T}^n$ being standard action--angle variables. 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