Symplectic diffeomorphisms and Weinstein 1-form.

In [5] the authors showed that the Liouville 1-form lying on the cotangent bundle is derived from physical potential and is related to the symplectomorphism through the ux homomorphism. On the other hand, in [7, 8], A. Weinstein constructed a chart from the group of symplectic diffeomorphisms isotopic to the identity by using Lagrangian sub-manifolds geometry and from which he derived a closed 1-form called the Weinstein 1-form. In this paper, we establish a relation between the Liouville 1-form and the Weinstein 1-form through an explicit formula from which we derive a new characterization of symplectomorphism and a new formula of the ux homomorphism. [ABSTRACT FROM AUTHOR]