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math.DS2025
On elementary integrability of rational vector fields
Colin Christopher, Sebastian Walcher
We consider complex rational vector fields that admit a first integral whose logarithmic derivative lies in a finite extension of the rational function field . In view of the Pr…
math.DS2025
Poincarè-Dulac Normal Forms: Formal and Analytic Aspects
Valery G. Romanovski, Sebastian Walcher
We discuss various aspects concerning transformations of local analytic, or formal, vector fields to Poincarè-Dulac normal form, and the convergence of such transformations. After…