Backward Error Analysis for Hamiltonian Splitting Methods

3 Backward Error Analysis for Hamiltonian Splitting Methods 

On the other hand, the splitting method based on a composition of flows on Hi and H2iS 

The issue then becomes the comparison of the exponential series 

Observe that, for any real-valued functions/ and H of phase space. 

This means that it is possible to relate the commutator of Lie derivatives of Hamiltonian vector fields to the Lie derivative of the Poisson bracket of the corresponding Hamiltonians, i.e., 

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