Hopf algebra techniques to handle dynamical systems and numerical integrators

Abstract

In a series of papers the present authors and their coworkers have developed a family of algebraic techniques to solve a number of problems in the theory of discrete or continuous dynamical systems and to analyze numerical integrators. Given a specific problem, those techniques construct an abstract, {\em universal} version of it which is solved algebraically; then, the results are tranferred to the original problem with the help of a suitable morphism. In earlier contributions, the abstract problem is formulated either in the dual of the shuffle Hopf algebra or in the dual of the Connes-Kreimer Hopf algebra. In the present contribution we extend these techniques to more general Hopf algebras, which in some cases lead to more efficient computations.