Galois differential algebras and categorical discretization of dynamical systems

A categorical theory for the discretization of a large class of dynamical systems with variable coefficients is proposed. It is based on the existence of covariant functors between the Rota category of Galois differential algebras and suitable categories of abstract dynamical systems. The integrable maps obtained share with their continuous counterparts a large class of solutions and, in the linear case, the Picard-Vessiot group.Comment: 19 pages (examples added

On the integrability of a system describing the stationary solutions in Bose--Fermi mixtures

We study the integrability of a Hamiltonian system describing the stationary solutions in Bose--Fermi mixtures in one dimensional optical lattices. We prove that the system is integrable only when it is separable. The proof is based on the Differential Galois approach and Ziglin-Morales-Ramis method.Comment: 21 page