Preserving first integrals and volume forms of additively split systems

@article{Chartier2007PreservingFI,
  title={Preserving first integrals and volume forms of additively split systems},
  author={Philippe Chartier and Ander Murua},
  journal={Ima Journal of Numerical Analysis},
  year={2007},
  volume={27},
  pages={381-405}
}
This work is concerned with the preservation of invariants and volume forms by numerical methods which can be expanded into B-series. The situation we consider here is that of a split vector field f = f [1] +... + f [N] , where each f [ν] either has the common invariant I or is divergence-free. We derive algebraic conditions on the coefficients of the B-series for it either to preserve I or to preserve the volume for generic vector fields and interpret them for additive Runge-Kutta methods… 
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Preserving algebraic invariants with Runge-Kutta methods
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