  The numerical method of Kahan applied to quadratic differential equations is
known to often generate integrable maps in low dimensions and can in more
general situations exhibit preserved measures and integrals. Computerized
methods based on discrete Darboux polynomials have recently been used for
finding these measures and integrals. However, if the differential system
contains many parameters, this approach can lead to highly complex results that
can be difficult to interpret and analyze. But this complexity can in some
cases be substantially reduced by using aromatic series. These are a
mathematical tool introduced independently by Chartier and Murua and by
Iserles, Quispel and Tse. We develop an algorithm for this purpose and derive
some necessary conditions for the Kahan map to have preserved measures and
integrals expressible in terms of aromatic functions. An important reason for
the success of this method lies in the equivariance of the map from vector
fields to their aromatic funtions. We demonstrate the algorithm on a number of
examples showing a great reduction in complexity compared to what had been
obtained by a fixed basis such as monomials.
