Discrete Mechanics, Geometric Integration and Lie-Butcher Series

Preface.- A. Iserles and G.R.W. Quispel , Why geometric numerical integration?.- B. Owren , Lie group integrators.- H. Z. Munthe-Kaas and K. K. Føllesdal , Lie-Butcher series, Geometry, Algebra and Computation.- A. Murua and J. M. Sanz-Serna , Averaging and computing normal forms with word series algorithms.- L. A. Duffaut Espinosa, K. Ebrahimi-Fard , and W. Steven Gray, Combinatorial Hopf algebras for interconnected nonlinear input-output systems with a view towards discretization.- F. Casas , Computational aspects of some exponential identities.- K. Ebrahimi-Fard and I. Mencattini , Post-Lie Algebras, Factorization Theorems and Isospectral Flows.- G. Bogfjellmo, R. Dahmen, and A.Schmeding , Overview of (pro-)Lie group structures on Hopf algebra character groups,.- M. Barbero Liñán and D. Martín de Diego , Bäcklund transformations in discrete variational principles for Lie-Poisson equations.- M. Vermeeren , Numerical precession in variational discretizations of the Kepler problem.- O. Verdier, Full affine equivariance and weak natural transformations in numerical analysis - the case of B-Series.- References.