
The present note is an announcement of ''results concerning the parametrization, in the sense of local moduli of the equivalence classes of a system of meromorphic differential equations of the form \(du/dz=Au\) near an irregular singular point (assumed to be \(z=0)\). Here u is an n- component column vector, A is an \(n\times n\) matrix of meromorphic functions''. The equivalence of analytic families of the system given by the above differential equation is studied and it is based in a fundamental way in the theory of formal equivalence over general rings developed by the authors in their monograph entitled ''Deformations of nilpotent matrices over rings and reduction of analytic families of meromorphic differential equations'', to be published in Mem. Am. Math. Soc.
34A20, Linear ordinary differential equations and systems, General theory of ordinary differential operators, irregular singular point, system of meromorphic differential equations, Entire and meromorphic solutions to ordinary differential equations in the complex domain, Entire and meromorphic functions of one complex variable, and related topics, formal equivalence over general rings
34A20, Linear ordinary differential equations and systems, General theory of ordinary differential operators, irregular singular point, system of meromorphic differential equations, Entire and meromorphic solutions to ordinary differential equations in the complex domain, Entire and meromorphic functions of one complex variable, and related topics, formal equivalence over general rings
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