We solve completely the problem of formal classification of the vector fields of the form x = y +. . ., y = . . . using formal changes of the coordinates but not of the time. In the proofs we avoid complicated calculations. The method we use is effective and can be applied in other classification problems.
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Stróżyna, E., & Żoladek, H. (2015). The complete formal normal form for the bogdanov–takens singularity. Moscow Mathematical Journal, 15(1), 141–178. https://doi.org/10.17323/1609-4514-2015-15-1-141-178