Abstract: In
this paper, we propose a new algorithm for an
effective computation of the Katz invariant of
a meromorphic differential system. This
algorithm is based on a method of deformation
of orbits under the adjoint representation of GL(n, C).The
essential step of this algorithm is so-called
Weak-Arnold form. This form has the same
effect as Arnold’s form in the algorithm of
Turritten-Wasow [Linear Algebra Appl. 18
(1977), 163-170]. Several examples showing
simplicity and efficiency of the suggested
method are given. Also, a comparison, by an
example, between the Turritten-Wasow’s
method and ours is given.
Keywords and phrases: singular differential systems, irregular singular point, Weak-Arnold form.
