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By semi-hyperbolic, we mean that the linearized Poincar{\\'e} map dP 0 associated with $\\gamma$ 0 has at least one eigenvalue of modulus greater (or less) than 1, and one eigenvalue of modulus equal to 1, and by non-degenerate that 1 is not an eigenvalue, which implies a family $\\gamma$(E) with the same "},"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":"1907.05630","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-12T08:54:42Z","cross_cats_sorted":[],"title_canon_sha256":"8cfba976b118d0a6fcaea13baa82bd42bc967a37b915bee9d7ea9c23ecce1b85","abstract_canon_sha256":"40dd3e30bbf7e30f235a269c9300bb223716f05dd73a52dddd29605a75353810"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:47.529680Z","signature_b64":"u1yEeOrWmiFNxywoqYWOjG26+b2VBSy7B86SiXaG9W7iCmV3FGz4nfMviTr/H1GCk5eb9LK0PD2J7VcIYvJdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a07f22812617d1d2349c65c76d14eb0c62e952bd9d373b501a66279a47c272eb","last_reissued_at":"2026-05-17T23:40:47.528936Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:47.528936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semi-classical quantum maps of semi-hyperbolic type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hanen Louati (CPT), Michel Rouleux (CPT)","submitted_at":"2019-07-12T08:54:42Z","abstract_excerpt":"Let M = R n or possibly a Riemannian, non compact manifold. 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