2026-04-17T04:12:33Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/1310432026-02-04T06:26:29Zcom_2072_1033col_2072_452950

urn:hdl:2117/131043 Coupling symmetries with Poisson structures Miranda Galcerán, Eva Laurent Gengoux, Camille Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals Poisson distribution Group actions Poisson manifolds Integrable systems Splitting theorem Equivariant Carathéodory–Jacobi–Lie theorem Coupling Poisson, Distribució de We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein’s splitting theorem for the integrable system is also studied giving some examples in which such a splitting does not exist, i.e. when the integrable system is not, locally, a product of an integrable system on the symplectic leaf and an integrable system on a transversal. The problem of splitting for integrable systems with additional symmetries is also considered. Peer Reviewed Postprint (published version) 2013 Article Restricted access - publisher's policy Springer