{"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 $S$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5358","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}