A new method.for the construction of integrable Hamiltonian system is proposed.For a given Poisson manifold the present paper constructs new Poisson brackets on it by making use of the Dirac-Poisson structure[1],and ...A new method.for the construction of integrable Hamiltonian system is proposed.For a given Poisson manifold the present paper constructs new Poisson brackets on it by making use of the Dirac-Poisson structure[1],and obtains .further new integrable Hamiltonian systems The constructed Poisson bracket is usual non-linear, and this new method is also different from usual ones[2-4].Two examples are given.展开更多
A sufficient and necessary condition is given for the action of the quotient of a Poisson-Lie group G on the quotient of a Poisson G-space P to be a Poisson action, where both the Poisson structures on the quotient gr...A sufficient and necessary condition is given for the action of the quotient of a Poisson-Lie group G on the quotient of a Poisson G-space P to be a Poisson action, where both the Poisson structures on the quotient group and the quotient manifold are induced by Dirac structures. The left invariant Dirac structure and the left invariant tensor descriptions of Poisson homogeneous spaces are proved to be equivalent.展开更多
基金Supported by Scientific Creative Platform Foundation of Beijing Municipal Commission of Education(No.PXM2008_014224_067420)Foundation of Beijing Information Science and Technology University
文摘A new method.for the construction of integrable Hamiltonian system is proposed.For a given Poisson manifold the present paper constructs new Poisson brackets on it by making use of the Dirac-Poisson structure[1],and obtains .further new integrable Hamiltonian systems The constructed Poisson bracket is usual non-linear, and this new method is also different from usual ones[2-4].Two examples are given.
文摘A sufficient and necessary condition is given for the action of the quotient of a Poisson-Lie group G on the quotient of a Poisson G-space P to be a Poisson action, where both the Poisson structures on the quotient group and the quotient manifold are induced by Dirac structures. The left invariant Dirac structure and the left invariant tensor descriptions of Poisson homogeneous spaces are proved to be equivalent.
