# A combinatorial approach to integrals of Kahan-Hirota-Kimura discretizations

@article{Zander2016ACA, title={A combinatorial approach to integrals of Kahan-Hirota-Kimura discretizations}, author={Ren'e Zander}, journal={arXiv: Exactly Solvable and Integrable Systems}, year={2016} }

We consider an Ansatz for the study of the existence of formal integrals of motion for Kahan-Hirota-Kimura discretizations. In this context, we give a combinatorial proof of the formula of Celledoni-McLachlan-Owren-Quispel for an integral of motion of the discretization in the case of cubic Hamiltonian systems on symplectic vector spaces and Poisson vector spaces with constant Poisson structure.

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