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We provide a result valid for general systems which are algebraic or trigonometric polynomials in the state variables. It consists on obtaining a rigorous proof of the asymptotic formula for the measure of the splitting. We obtain that the splitting has the asymptotic behavior $K \\varepsilon^{\\beta} \\text{e}^{-a/\\varepsilon}$, identifying the constants $K,\\beta,a$ in terms of the system features.\n  We consider"},"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":"1201.5152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-24T22:54:50Z","cross_cats_sorted":[],"title_canon_sha256":"b5862aa4707bca0291fa3bbe8c7d3684558c9a7c5216921ac5a54afebc36b08e","abstract_canon_sha256":"8b8e8fd82f430526b3556174f728b14a348962b7835c6c7634433bb14497fde0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:55.470847Z","signature_b64":"F/PQKdZYhL7k5gcCJAZsDCV1CroHJ/sSv85LLx+lX5xpPcHqrKEoft2IJ+mb+8jjkcaMyIkGuGapwfI+6nayCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42eaccce5365656acf3c924500924e407743af1b44836238bc3479a525aa7f2c","last_reissued_at":"2026-05-18T04:03:55.470383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:55.470383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponentially small splitting of separatrices beyond Melnikov analysis: rigorous results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ernest Fontich, Inmaculada Baldoma, Marcel Guardia, Tere M. 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