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.

We develop a framework for dealing with smooth approximations to billiards with corners in the two-dimensional setting. Let a polygonal trajectory in a billiard start and end up at the same billiard’s corner point. We prove that smooth Hamiltonian flows which limit to this billiard have a nearby periodic orbit if and only if the polygon angles at the corner are ‘‘acceptable.’’ The criterion for...

The Eringen’s nonlocal elastica equation does not possess a Lagrangian formulation. In this article, we find variational integrating factor which enables us to provide and Hamiltonian structure associated equation. Explicit expressions of the solutions in terms elliptic integrals first kind are then deduced. We derive discrete version preserving compare it with Challamel’s co-worker definition ...

We revisit an algorithm constructing elliptic tori, that was originally designed for applications to planetary hamiltonian systems. The scheme is adapted properly work with models of chains $N+1$ particles interacting via anharmonic potentials, thus covering also the case FPU chains. After having preliminarily settled Hamiltonian in a suitable way, we perform sequence canonical transformations ...

The eigenvalues of the Corner Transfer Matrix Hamiltonian associated to the el-liptic R matrix of the eight vertex free fermion model are computed in the anisotropic case for magnetic eld smaller than the critical value. An argument based on generating functions is given, and the results are checked numerically. The spectrum consists of equally spaced levels.