## 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.

### MSC:

 13N99 Differential algebra
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### References:

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