Convergence of Lie group integrators

We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we prove for the first time that the Lie-Butcher theory of Lie group integrators leads to global error estimates.
Comment: 18 pages, uses TikZ, v2: corrected typos and minor errors, main results remain unchanged