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

Coupling symmetries with Poisson structures Miranda Galcerán, Eva Laurent Gengoux, Camille Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions 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 Miranda, E.; Laurent-Gengoux, C. Coupling symmetries with Poisson structures. "Acta Mathematica Vietnamica", 2013, vol. 38, núm. 1, p. 21-32. 0251-4184 https://hdl.handle.net/2117/131043 10.1007/s40306-013-0008-1 eng Restricted access - publisher's policy 12 p. application/pdf Springer