Displaying similar documents to “Semi-formal theory and Stokes' phenomenon of non-linear meromorphic systems of ordinary differential equations”

Stokes phenomenon, multisummability and differential Galois groups

Michèle Loday-Richaud (1994)

Annales de l'institut Fourier

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We precise the cohomological analysis of the Stokes phenomenon for linear differential systems due to Malgrange and Sibuya by making a rigid natural choice of a unique cocycle (called a Stokes cocyle) in every cohomological class. And we detail an algebraic algorithm to reduce any cocycle to its cohomologous Stokes form. This gives rise to an almost algebraic definition of sums for formal solutions of systems which we compare to the most usual ones. We also use this construction to the...

Further remarks on formal power series

Marcin Borkowski, Piotr Maćkowiak (2012)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we present a considerable simplification of the proof of a theorem by Gan and Knox, stating a sufficient and necessary condition for existence of a composition of two formal power series. Then, we consider the behavior of such series and their (formal) derivatives at the boundary of the convergence circle, obtaining in particular a theorem of Bugajewski and Gan concerning the structure of the set of points where a formal power series is convergent with all its derivatives. ...