First Integrals Generated by Pseudosymmetries in Nambu-Poisson Mechanics

First Integrals Generated by Pseudosymmetries in Nambu - Poisson Mechanics

Some types of first integrals for Hamiltonian Nambu-Poisson vector fields are obtained by using the notions of pseudosymmetries. In this theory, the homogeneous Hamilto-nian vector fields play a special role and we point out this fact. The differential system which describe the SU (2)-monopoles is given as example. The paper ends with two appendices.

Computations of Nambu-Poisson cohomologies

In this paper, we want to associate to a n-vector on a manifold of dimension n a cohomology which generalizes the Poisson cohomology of a 2-dimensional Poisson manifold. Two possibilities are given here. One of them, the Nambu-Poisson cohomology, seems to be the most pertinent. We study these two cohomologies locally, in the case of germs of n-vectors on Kn (K = R or C).

Poisson geometry and first integrals of geostrophic equations

We describe first integrals of geostrophic equations, which are similar to the enstrophy invariants of the Euler equation for an ideal incompressible fluid. We explain the geometry behind this similarity, give several equivalent definitions of the Poisson structure on the space of smooth densities on a symplectic manifold, and show how it can be obtained via the Hamiltonian reduction from a sym...

Dynamics of generalized Poisson and Nambu–Poisson brackets

Nonabsolutely convergent Poisson integrals

If a function f has finite Henstock integral on the boundary of the unit disk of R 2 then its Poisson integral exists for |z| < 1 and is o((1 − |z|) −1) as |z| → 1 −. It is shown that this is the best possible uniform pointwise estimate. For an L 1 measure the best estimate is O((1 − |z|) −1). In this paper we consider estimates of Poisson integrals on the unit circle with respect to Alexiewicz...