Principle of galois theory.
We proposed a general Galois Theory of differential equations in char. 0 in 1996. The principle in this theory works also in different contexts. Namely (1) Difference equations in char. 0, (2) Differential equation in char. p > 0, (3) Difference equation in char. p > 0. General Galois Theory allows us to analyze group theoretically integrability of dynamical systems on algebraic varieties defined over a field of char. p > 0 as well as char. 0.