The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system. The abstract moment map is defined from G-manifold M to dual Lie algebra of G. We will interested study maps from G-manifold M to spaces that are more general than dual Lie algebra of G. These maps help us to reduce the dimension of a manifold much more. Manuscript profile

The primary aim of this paper is to investigate useful generalizations of the classical concept of action of a hyperstructure on a non-empty set. The main goal is to develop the theory of dynamical system to the theory of $n$-ary dynamical hypersystem. We also give some principal properties of an $n$-ary dynamical hypersystem. Manuscript profile