In the expressions
is the vector computed in (57) and
(branch parameter) is a component of
.
In the second expression , we compute
by solving
So the third expression for the normal form coefficient becomes
In the fourth expression, is the monodromy matrix.
In the fifth expression, is the
matrix that restricts the
matrix
to the space orthogonal to the two-dimensional left eigenspace of the two multipliers that are closest to
.
The number of branch parameters is not fixed. If the number of branch parameters is then this matrix has three more rows and columns. This singularity matrix is automatically extended: