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We investigate ergodic properties of these infinite measure-preserving flows and prove that if $f$ belongs to a space of finite codimension in $\\mathscr{C}^{2+\\epsilon}(S)$, then the following dynamical d"},"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":"1102.5358","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-25T21:50:02Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"aadafc3f20c60232c3ac1a6b5941d64f0de4fcf2e4eb59249cff995b3a88c21e","abstract_canon_sha256":"14ee6343b7ef1db2c3ce5f50b99650e44dd62961070be47e216465f85dfcc241"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:52:13.051933Z","signature_b64":"QIyYdqB7VOE428OG0XUr72MEp09U61A/EPEVbZK61eNZAVToXNrzJ0qIS+sCDiT97LBKywBbbblMVYuE7EbuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32996eefa67d79f8d9a67d45a9853c92f9fe2bdee7df31c67ef92850175e0118","last_reissued_at":"2026-05-18T02:52:13.051342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:52:13.051342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ergodic properties of infinite extensions of area-preserving flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Corinna Ulcigrai, Krzysztof Fraczek","submitted_at":"2011-02-25T21:50:02Z","abstract_excerpt":"We consider volume-preserving flows $(\\Phi^f_t)_{t\\in\\mathbb{R}}$ on $S\\times \\mathbb{R}$, where $S$ is a closed connected surface of genus $g\\geq 2$ and $(\\Phi^f_t)_{t\\in\\mathbb{R}}$ has the form $\\Phi^f_t(x,y)=(\\phi_tx,y+\\int_0^t f(\\phi_sx)ds)$, where $(\\phi_t)_{t\\in\\mathbb{R}}$ is a locally Hamiltonian flow of hyperbolic periodic type on $S$ and $f$ is a smooth real valued function on $S$. 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