On extensions, Lie-Poisson systems, and dissipation

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dc.authorid0000-0002-6766-0287
dc.authorid0000-0003-0925-8668
dc.contributor.authorEsen, Oğulen_US
dc.contributor.authorÖzcan, Gökhanen_US
dc.contributor.authorSütlü, Serkanen_US
dc.date.accessioned2025-10-08T06:48:07Z
dc.date.available2025-10-08T06:48:07Z
dc.date.issued2021-01-08
dc.departmentIşık Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümüen_US
dc.departmentIşık University, Faculty of Engineering and Natural Sciences, Department of Mathematicsen_US
dc.descriptionThis paper is a part of the project Matched pairs of Lagrangian and Hamiltonian Systems supported by TUBITAK (the Scientific and Technological Research Council of Turkey) withthe project number 117F426. All of the authors are grateful to TUBITAK for the support.en_US
dc.description.abstractOn the dual space of extended structure, equations governing the collective motion of two mutually interacting Lie-Poisson systems are derived. By including a twisted 2-cocycle term, this novel construction is providing the most general realization of (de)coupling of Lie-Poisson systems. A double cross sum (matched pair) of 2-cocycle extensions are constructed. The conditions are determined for this double cross sum to be a 2-cocycle extension by itself. On the dual spaces, Lie-Poisson equations are computed. We complement the discussion by presenting a double cross sum of some symmetric brackets, such as double bracket, Cartan-Killing bracket, Casimir dissipation bracket, and Hamilton dissipation bracket. Accordingly, the collective motion of two mutually interacting irreversible dynamics, as well as mutually interacting metriplectic flows, are obtained. The theoretical results are illustrated in three examples. As an infinite-dimensional physical model, decompositions of the BBGKY hierarchy are presented. As finite-dimensional examples, the coupling of two Heisenberg algebras and coupling of two copies of 3D dynamics are studied.en_US
dc.description.sponsorshipTÜBİTAKen_US
dc.description.versionPreprint's Versionen_US
dc.identifier.citationEsen, O. Özcan, G. & Sütlü, S. (2021). On extensions, Lie-Poisson systems, and dissipation. Arxiv, 1-55. doi:https://doi.org/10.48550/arXiv.2101.03951en_US
dc.identifier.endpage55
dc.identifier.startpage1
dc.identifier.urihttps://hdl.handle.net/11729/6753
dc.identifier.urihttps://doi.org/10.48550/arXiv.2101.03951
dc.identifier.wosPPRN:10473273
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakPreprint Citation Indexen_US
dc.institutionauthorSütlü, Serkanen_US
dc.institutionauthorid0000-0003-0925-8668
dc.language.isoenen_US
dc.publisherCornell Univen_US
dc.relation.ispartofArxiven_US
dc.relation.publicationcategoryÖn Baskı – Uluslararası – Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectLie-Poisson equationen_US
dc.subjectMetriplectic systemen_US
dc.subjectExtended structureen_US
dc.titleOn extensions, Lie-Poisson systems, and dissipationen_US
dc.typePreprinten_US
dspace.entity.typePublicationen_US

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