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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Poisson Brackets after Jacobi and Plücker
Pantelis A. Damianou Department of Mathematics and Statistics, University of Cyprus,
P.O. Box 20537, 1678 Nicosia, Cyprus
Аннотация:
We construct a symplectic realization and a bi-Hamiltonian formulation of a 3-dimensional system whose solution are the Jacobi elliptic functions. We generalize this system and the related Poisson brackets to higher dimensions. These more general systems are parametrized by lines in projective space. For these rank 2 Poisson brackets the Jacobi identity is satisfied only when the Plücker relations hold. Two of these Poisson brackets are compatible if and only if the corresponding lines in projective space intersect. We present several examples of such systems.
Ключевые слова:
Poisson structures, Plücker relations.
Поступила в редакцию: 12.09.2018 Принята в печать: 15.10.2018
Образец цитирования:
Pantelis A. Damianou, “Poisson Brackets after Jacobi and Plücker”, Regul. Chaotic Dyn., 23:6 (2018), 720–734
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd362 https://www.mathnet.ru/rus/rcd/v23/i6/p720
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