{"id":323,"date":"2026-09-29T09:22:21","date_gmt":"2026-09-29T07:22:21","guid":{"rendered":"https:\/\/project.inria.fr\/cfd60ai\/?page_id=323"},"modified":"2026-09-29T09:29:37","modified_gmt":"2026-09-29T07:29:37","slug":"dsipp","status":"publish","type":"page","link":"https:\/\/project.inria.fr\/cfd60ai\/dsipp\/","title":{"rendered":""},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center\"><strong>Denis Sipp<\/strong><\/h2>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">ONERA &#8211; \ud83c\uddeb\ud83c\uddf7 Palaiseau (France)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center\">Koopman representations of decaying correlations: A deterministic route from continuous spectra to finite pole models<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Decaying correlations in chaotic deterministic systems cannot generally be described by damped Koopman eigenfunctions in the natural <math data-latex=\"L^2 \"><semantics><msup><mi>L<\/mi><mn>2<\/mn><\/msup><annotation encoding=\"application\/x-tex\">L^2 <\/annotation><\/semantics><\/math> space, since the Koopman group is unitary and its generator is skew-adjoint. This presentation examines how finite-dimensional models with damped poles nevertheless emerge from such dynamics. Two complementary routes are developed: meromorphic continuation of the weak correlation resolvent, leading to Ruelle\u2013Pollicott resonances, and Mori\u2013Zwanzig projection, where unresolved dynamics generate a memory term. Rational approximation of either the continued resolvent or the memory kernel then yields a finite realization of the correlation dynamics. The framework is illustrated using cavity-flow measurements, with particular attention to distinguishing robust isolated resonances from finite-order approximations of a continuous spectral background.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Denis Sipp ONERA &#8211; \ud83c\uddeb\ud83c\uddf7 Palaiseau (France) Koopman representations of decaying correlations: A deterministic route from continuous spectra to finite pole models Decaying correlations in chaotic deterministic systems cannot generally be described by damped Koopman eigenfunctions in the natural L2L^2 space, since the Koopman group is unitary and its generator\u2026<\/p>\n<p> <a class=\"continue-reading-link\" href=\"https:\/\/project.inria.fr\/cfd60ai\/dsipp\/\"><span>Continue reading<\/span><i class=\"crycon-right-dir\"><\/i><\/a> <\/p>\n","protected":false},"author":2613,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_members_access_role":[],"_members_access_error":""},"class_list":["post-323","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/pages\/323","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/users\/2613"}],"replies":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/comments?post=323"}],"version-history":[{"count":2,"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/pages\/323\/revisions"}],"predecessor-version":[{"id":326,"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/pages\/323\/revisions\/326"}],"wp:attachment":[{"href":"https:\/\/project.inria.fr\/cfd60ai\/wp-json\/wp\/v2\/media?parent=323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}