The Cartan-Tresse linearization polynomial and applications. (English) Zbl 1154.13009

The authors study differential equations of the form \(P(x,y,y')=0\) where \(P\) is a polynomial. The Cartan-Tresse linearization polynomial is a differential polynomial which is defined in order to tell whether \(P\) is linearizable, i.e. whether after a suitable holomorphic change of coordinates the integral curves of the equation become (germs of) straight lines. The authors study the influence of the Cartan-Tresse linearization polynomial in some classical problems of analysis, differential algebra and geometry, such as singular solutions, the Ritt problem or webs theory.


13N99 Differential algebra
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