Reversible Perturbation Theory and Symmetric Integrators

Abstract

Numerical experiments indicate that symmetric methods applied to integrable and near-integrable reversible systems share similar properties to symplectic methods applied to (near-)integrable Hamiltonian systems: linear error growth, long-time near-conservation of first integrals, existence of invariant tori. The present chapter gives a theoretical explanation of the good long-time behaviour of symmetric methods. The results and techniques are largely analogous to those of the previous chapter – the extent of the analogy may indeed be seen as the most surprising feature of this chapter.