It is shown that to every Archimedean copula H there corresponds a one-parameter semigroup of transformations of the interval [0,1]. If the elements of the semigroup are diffeomorphisms, then it determines a special function $v_H$ called the vector generator. Its knowledge permits finding a pseudoinverse y = h(x) of the additive generator of the Archimedean copula H by solving the differential equation $dy/dx=v_H\left(y\right)/x$ with initial condition $(dh/dx)\left(0\right)=-1$. Weak convergence of Archimedean copulas is characterized in terms of vector...