Geodesic
Convergence of formal Dulac series satisfying an algebraic ordinary differential equation
Sbornik. Mathematics, Tome 210 (2019) no. 9, pp. 1207-1221

Voir la notice de l'article provenant de la source Math-Net.Ru

A sufficient condition is proposed which ensures that a Dulac series that formally satisfies an algebraic ordinary differential equation (ODE) is convergent. Such formal solutions of algebraic ODEs are quite common: in particular, the Painlevé III, V and VI equations have formal solutions given by Dulac series; they are convergent in view of the sufficient condition presented. Bibliography: 13 titles.
Keywords: Dulac series
Mots-clés : algebraic ODE, formal solution, convergence. 
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     author = {R. R. Gontsov and I. V. Goryuchkina},
     title = {Convergence of formal {Dulac} series satisfying an algebraic ordinary differential equation},
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     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_9_a0/}
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R. R. Gontsov; I. V. Goryuchkina. Convergence of formal Dulac series satisfying an algebraic ordinary differential equation. Sbornik. Mathematics, Tome 210 (2019) no. 9, pp. 1207-1221. http://geodesic.mathdoc.fr/item/SM_2019_210_9_a0/