ABSTRACT
The geometric numerical integrators introduced in Chapter 1, such as the symplectic Euler schemes and the Störmer–Verlet methods, provide, in spite of their low order of accuracy, a fairly good qualitative description of dynamical systems possessing distinctive geometric features. Although this low order does not constitute a hindrance for, say, molecular dynamics applications, there are other important areas of applications where a higher degree of precision is very welcome in addition to the preservation of qualitative properties. A familiar example is the long-term numerical integration of the Solar System, both forward (to analyze e.g. the existence of chaos [155, 245]) and backward in time (to study the insolation quantities of the Earth [158]).
