Algorithms for formal reduction of vector field singularities
The authors present several algorithms transforming a Pfaffian form of the type \(\omega = d(y^2 - x^q) + \delta(x, y) (2x +dy - qydx)\) into the normal form given by \textit{F. Loray} [J. Differ. Equations 158, 152-173 (1999; Zbl 0985.37014)] in the cases \(q = 2\) and \(q =3\). The main results give a numerical answer to the question on the convergence of normal forms. For \( q =3\), in the nondegenerate case, their numerical analysis of algorithms leads to Gevrey estimates of order 2. Moreover, in the case \(q =2\), their results agree with the results of \textit{J. Martinet} and \textit{J.-P. Ramis} [Ann. Sci. Éc. Norm. Supér. 16, 571-621 (1983; Zbl 0534.34011)].
scientific article; zbMATH DE number 1901425