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We suppose that $N$ is controllable and that its stable and unstable bundles are trivial. We consider a $C^1$-submanifold $\\d$ of $M$ whose dimension is equal to the dimension of a fiber of the unstable bundle of $T_NM$. We suppose that $\\d$ transversely intersects the stable manifold of $N$. Then, we prove that for all $\\varepsilon>0$, and for $n$ $\\in$ $\\N$ large eno"},"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":"1302.4311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-18T15:24:32Z","cross_cats_sorted":[],"title_canon_sha256":"4381f97efdbfef1c43bfe07a087eee8bf9fb1a11f61529334982b1bc0ab3acc4","abstract_canon_sha256":"afcd4ebad6713888a9f5e3b8118c45883e97c875c59164bfbcc4f2aa6b795713"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:31.897712Z","signature_b64":"pJ86w39LnTHaIumkiP156R7RkGeIij2HuEe3QuTK8ETmEuhbmrlHc03FGJWiwFW5RsDclTz1nloF+x/p6Mg9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12211b891a21c113701e975cd3c00c991c7f78b26487a65929962596b3de0150","last_reissued_at":"2026-05-18T02:47:31.897245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:31.897245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An inclination lemma for normally hyperbolic manifolds with an application to diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lara Sabbagh","submitted_at":"2013-02-18T15:24:32Z","abstract_excerpt":"Let ($M$, $\\Omega$) be a smooth symplectic manifold and $f:M\\rightarrow M$ be a symplectic diffeomorphism of class $C^l$ ($l\\geq 3$). Let $N$ be a compact submanifold of $M$ which is boundaryless and normally hyperbolic for $f$. We suppose that $N$ is controllable and that its stable and unstable bundles are trivial. We consider a $C^1$-submanifold $\\d$ of $M$ whose dimension is equal to the dimension of a fiber of the unstable bundle of $T_NM$. We suppose that $\\d$ transversely intersects the stable manifold of $N$. 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