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

Sums and averages

These informal notes are concerned with sums and averages in various situations in analysis.Comment: 51 page