Arithmetic differential equations and complete integrability

The theory of differential equations has an arithmetic analogue in which derivatives of functions are replaced by Fermat quotients of numbers. Many classical differential equations(Riccati, Weierstrass, Painleve', etc.) were previously shown to possess arithmetic analogues. The talk is devoted to the study
of an arithmetic analogue of the Euler differential equations for the rigid body and possible links
with more general completely integrable systems.