Displaying similar documents to “Recent progress in the integration of Poisson systems via the mid-point rule and Runge-Kutta algorithm.”

Nambu-Poisson Tensors on Lie Groups

Nobutada Nakanishi (2000)

Banach Center Publications

Similarity:

First as an application of the local structure theorem for Nambu-Poisson tensors, we characterize them in terms of differential forms. Secondly left invariant Nambu-Poisson tensors on Lie groups are considered.

Some Remarks on Dirac Structures and Poisson Reductions

Zhang-Ju Liu (2000)

Banach Center Publications

Similarity:

Dirac structures are characterized in terms of their characteristic pairs defined in this note and then Poisson reductions are discussed from the point of view of Dirac structures.

Poisson Lie groups and their relations to quantum groups

Janusz Grabowski (1995)

Banach Center Publications

Similarity:

The notion of Poisson Lie group (sometimes called Poisson Drinfel'd group) was first introduced by Drinfel'd [1] and studied by Semenov-Tian-Shansky [7] to understand the Hamiltonian structure of the group of dressing transformations of a completely integrable system. The Poisson Lie groups play an important role in the mathematical theories of quantization and in nonlinear integrable equations. The aim of our lecture is to point out the naturality of this notion and to present basic...

Normal forms of vector fields on Poisson manifolds

Philippe Monnier, Nguyen Tien Zung (2006)

Annales mathématiques Blaise Pascal

Similarity:

We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.

Mixed formulation for elastic problems - existence, approximation, and applications to Poisson structures

Julian Ławrynowicz, Alain Mignot, Loucas Papaloucas, Claude Surry (1996)

Banach Center Publications

Similarity:

A mixed formulation is given for elastic problems. Existence and uniqueness of the discretized problem are given for conformal continuous interpolations for the stress tensor components and for the components of the displacement vector. A counterpart of the problem is discussed in the case of an even-dimensional Euclidean space with an associated Hamiltonian vector field and the Poisson structure. For conformal interpolations of the same order the question remains open.