We discuss the Mattei-Moussu topological criterion for existence of a holomorphic first integral in a neighbourhood of a singular point of an analytic differential equation, and we prove that it cannot be used to get algebraic solvability of such an existence problem.
On the problem of existence of holomorphic first integrals / Villarini, Massimo. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - 194:(1995), pp. 799-822.
On the problem of existence of holomorphic first integrals
VILLARINI, Massimo
1995
Abstract
We discuss the Mattei-Moussu topological criterion for existence of a holomorphic first integral in a neighbourhood of a singular point of an analytic differential equation, and we prove that it cannot be used to get algebraic solvability of such an existence problem.
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