Integrability of Hamiltonian systems on COLCS Manifold

[2608.14699] Integrability of Hamiltonian systems on COLCS Manifold Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematical Physics arXiv:2608.14699 (math-ph) [Submitted on 10 Aug 2026] Title: Integrability of Hamiltonian systems on COLCS Manifold Authors: Antonio J. Pan-Collantes , Xuefeng Zhao View a PDF of the paper titled Integrability of Hamiltonian systems on COLCS Manifold, by Antonio J. Pan-Collantes and Xuefeng Zhao View PDF HTML (experimental) Abstract: We develop an integrability framework for Hamiltonian dynamics on \emph{con-locally conformal symplectic} (COLCS) manifolds, odd-dimensional quadruples $(M,\Omega,\theta,\eta)$ where $d\Omega=\theta\wedge\Omega$, a closed $1$-form $\eta$ determines a codimension-one distribution on which $\Omega$ is non-degenerate, and $R$ is the Reeb vector field satisfying $\iota_R\Omega=\iota_R\theta=0$, $\iota_R\eta=1$. This class simultaneously generalises LCS and cosymplectic manifolds and provides a natural arena for time-dependent Hamiltonian systems with twisted differential $d^\theta=d-\theta\wedge$. The COLCS bracket is introduced on $C^\infty(M)$ and shown to be a Lie bracket that induces Poisson structures on the subalgebras of $\theta$-strong ($\theta(X_H)=0$) and $R$-strong ($R(H)=0$) functions. A Lie-type integrability theorem is then established: given $2n-k$ functionally independent first integrals with $k$ of them $\theta$-strong and generating a solvable Lie algebra under the COLCS bracket, the flow is integrable by quadratures on the common level set. Finally, scaling symmetries of degree $(\Lambda,\beta,\gamma)$, defined by $L_X\Omega=\beta\Omega$, $L_XH=\Lambda H$, $L_X\eta=\gamma\eta$, are studied: they rescale $X_H$ by $(\Lambda-\beta)$, generate families of first integrals, and imply structural primitives for $\Omega$ and $\eta$. Subjects: Mathematical Physics (math-ph) Cite as: arXiv:2608.14699 [math-ph] (or arXiv:2608.14699v1 [math-ph] for this version) https://doi.org/10.48550/arXiv.2608.14699 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Xuefeng Zhao [ view email ] [v1] Mon, 10 Aug 2026 02:46:49 UTC (19 KB) Full-text links: Access Paper: View a PDF of the paper titled Integrability of Hamiltonian systems on COLCS Manifold, by Antonio J. Pan-Collantes and Xuefeng Zhao View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2026-08 Change to browse by: math math.MP References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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