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The strength of the perturbation is given by a parameter $\\epsilon\\in\\mathbb{R}$. For all $|\\epsilon|$ sufficiently small, the augmented flow has a $(2d + 1)$-dimensional normally hyperbolic locally invariant manifold $\\tilde\\Lambda_\\epsilon$.\n  We define a Melnikov vector, which gives the first order expansion of the displacement of the stable and unstable manifolds"},"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":"1710.01849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-10-05T01:14:14Z","cross_cats_sorted":["math-ph","math.MP","math.SG","nlin.CD"],"title_canon_sha256":"2ac6a34dbd06c8fc5c82e5a89d6d7fb5211ac1ac2c13d2798d39f14b9dcf45a7","abstract_canon_sha256":"32b961635ba8ee146f75e8e7b47f728bbf401e7391ecc5c4495444ad78f3b8c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:31.058849Z","signature_b64":"b/b2UnjaWkrwot4g9TZkH0AF5J7iO4rNeq9HK8WFMl7uABK5UQWirDuFN2GbTOTj6MVPihN+VuMtj3tZ7ckVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f19513bf08456f8c24fdb72b9d63a5fe29c99ac51be2fa7329b7f9474d221a40","last_reissued_at":"2026-05-18T00:16:31.058326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:31.058326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Melnikov Theory in Hamiltonian Systems with General Time-dependent Perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SG","nlin.CD"],"primary_cat":"math.DS","authors_text":"Marian Gidea, Rafael de la Llave","submitted_at":"2017-10-05T01:14:14Z","abstract_excerpt":"We consider a mechanical system consisting of $n$ penduli and a $d$-dimensional generalized rotator subject to a time-dependent perturbation. 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