Abstract:
Birkhoff's reduction problem is to find an analytic or meromorphic transformation reducing a linear system of meromorphic ordinary differential equations to a form in which the coefficients are polynomials. This article is a survey of existing results, with several new results stated. In particular, it is shown that every irreducible system with an unramified formal fundamental solution can be transformed meromorphically into Birkhoff standard form, that is, to a system of minimal Poincaré rank and with normalized eigenvalues at the origin.
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