GENERALIZED n-POISSON BRACKETS ON A SYMPLECTIC MANIFOLD

A Note on n-ary Poisson Brackets

A class of n-ary Poisson structures of constant rank is indicated. Then, one proves that the ternary Poisson brackets are exactly those which are defined by a decomposable 3-vector field. The key point is the proof of a lemma which tells that an n-vector (n ≥ 3) is decomposable iff all its contractions with up to n− 2 covectors are decomposable. In the last years, several authors have studied g...

Dimensional Reduction for Generalized Poisson Brackets

We discuss dimensional reduction for Hamiltonian systems which possess nonconstant Poisson brackets between pairs of coordinates and between pairs of momenta. The associated Jacobi identities imply that the dimensionally reduced brackets are always constant. Some examples are given alongside the general theory.

Dynamics of generalized Poisson and Nambu–Poisson brackets

Generalized Reduction Procedure: Symplectic and Poisson Formalism

We present a generalized reduction procedure which encompasses the one based on the momentum map and the projection method. By using the duality between manifolds and ring of functions defined on them, we have cast our procedure in an algebraic context. In this framework we give a simple example of reduction in the non-commutative setting. Partially supported by the Italian Consiglio Nazionale ...

Differential-geometric Poisson Brackets on a Lattice

The concept of differential-geometric Poisson brackets (DGPB) was introduced in [i] in connection with an investigation of the properties of Poisson brackets of hydrodynamic type [2] and their generalizations. Recall that homogeneous DGPBs of m-th order on a phase space of fields u i @),i = i ..... N,x ~ ~ (in this note we confine attention to the spatially onedimensional case), taking values i...