Summary
An analysis of global aspects of the theory of symmetry groupsG of locally Hamiltonian dynamical systems is carried out for particular cases either of the symmetry group, or the differentiable manifoldM supporting the symplectic structure, or the action ofG onM. In every case we obtain a generalization of Noether's theorem. We also look at the classical Noether's theorem for Lagrangian systems from a modern perspective.
Riassunto
Si esegue un'analisi degli aspetti globali della teoria dei gruppi di simmetriaG di sistemi dinamici localmente hamiltoniani per casi particolari sia del gruppo di simmetria che della varietà differenziabileM in supporto della struttura simplettica che dell'azione diG suM. In ogni caso si ottiene una generalizzazione del teorema di Noether. Si esamina anche il teorema classico di Noether per sistemi lagrangiani secondo una prospettiva moderna.
Резюме
Проводится анализ глобальных аспектов теории групп симметрииG локально гамильтоновых систем для частых случаев либо группы симметрии, либо дифференцируемого множестваM, поддерживающего симплексную структуру или действиеG наM. В каждом случае мы получаем обобщение теоремы Ноэтера. Мы также анализируем классическую теорему Ноэтера для лагранжевых систем с современной точки зрения.
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Cariñena, J.F., Ibort, L.A. Locally hamiltonian systems with symmetry and a generalized Noether's theorem. Nuov Cim B 87, 41–49 (1985). https://doi.org/10.1007/BF02729240
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DOI: https://doi.org/10.1007/BF02729240