Generalized Hamilton system is defined by generalized Poisson bracket, the Poisson bracket is an important binary operation in Hamiltonian mechanics, playing a central role in Hamilton's equations of motion,. In the paper, Combinatorial operator η in 1-form space ( ) P Λ on Poisson manifold P is constructed and sufficient and necessary conditions that the vector field which induced by 1-form is...

The dynamics of Vlasov kinetic moments is shown to be Lie-Poisson on the dual Lie algebra of symmetric contravariant tensor fields. The corresponding Lie bracket is identified with the symmetric Schouten bracket and the moment Lie algebra is related with a bundle of bosonic Fock spaces, where creation and annihilation operators are used to construct the cold plasma closure. Kinetic moments are ...

In this paper we show that Poisson brackets linked to geometric flows of curves on flat Riemannian manifolds are Poisson reductions of the Kac–Moody bracket of SO(n). The bracket is reduced to submanifolds defined by either the Riemannian or the natural curvatures of the curves. We show that these two cases are (formally) Poisson equivalent and we give explicit conditions on the coefficients of...

Reduction in the category of Poisson manifolds is defined and some basic properties are derived. The context is chosen to include the usual theorems on reduction of symplectic manifolds, as well as results such as the Dirac bracket and the reduction to the Lie-Poisson bracket.

It is shown that the dual of the double compactified D=11 Supermembrane and a suitable compactified D=10 Super 4D-brane with nontrivial wrapping on the target space may be formulated as noncommutative gauge theories. The Poisson bracket over the world-volume is intrinsically defined in terms of the minima of the hamiltonian of the theory, which may be expressed in terms of a non degenerate 2-fo...

From the Hamiltonian structure of the Vlasov equation, we build a Hamiltonian model for the first three moments of the Vlasov distribution function, namely, the density, the momentum density and the specific internal energy. We derive the Poisson bracket of thismodel from the Poisson bracket of the Vlasov equation, andwe discuss the associated Casimir invariants. © 2014 Elsevier Inc. All rights...

We extend the Nambu bracket to 1-forms. Following the Poisson-Lie case, we define Nambu-Lie groups as Lie groups endowed with a multiplica-tive Nambu structure. A Lie group G with a Nambu structure P is a Nambu-Lie group iff P = 0 at the unit, and the Nambu bracket of left (right) invariant forms is left (right) invariant. We define a corresponding notion of a Nambu-Lie algebra. We give several...

We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation of differential equations of mathematical physics. Fractionality is obtained by substituting the ordinary integer-order derivative with the Caputo fractional ...