In this article, we study the existence and multiplicity of nontrivial solutions for a class of Hamiltoniam systems with weights and nonlinearity involving the Hardy-Sobolev exponents. Results are proved using variational methods for strongly indefinite functionals.

We obtain a bifurcation result for solutions of the Lorentz equation in a semiRiemannian manifold; such solutions are critical points of a certain strongly indefinite functionals defined in terms of the semi-Riemannian metric and the magnetic field. The flow of the Jacobi equation along each solution preserves the so-called magnetic symplectic form, and the corresponding curve in the symplectic...