Hamiltonian formalism of homogeneous cosmological model of type IX with electromagnetic field

The Einstein–Maxwell equations for a homogeneous cosmological model of type IX with electromagnetic field are reduced to a Hamiltonian system with constraints. It is shown that the constraints are zero levels of integrals of the energy and the moments; an additional first integral is found. An investigation is made of the oscillatory regime of the behavior of solutions with diagonal metric and singlecomponent electromagnetic field near the cosmological singularity, and the differences between it and the analogous regime for vacuum solutions are pointed out.