SEMINAIRE Mulhousien de MATHEMATIQUES

résumé/abstract


            David Sauzin (CNRS, l’Observatoire de Paris)

Initiation to mould calculus through the example of saddle-node singularities

 

Ecalle's mould calculus is a powerful combinatorial tool which yields surprisingly explicit formulas for the normalising series attached to an analytic germ of singular vector field, by manipulating formal sums of operators. We shall illustrate it on the case of saddle-node singularities, generated by two-dimensional vector fields which are formally conjugate to Euler's vector field $x2\frac{\pa}{\pa x}+(x+y)\frac{\pa}{\pa y}$, and for which the formal normalisation proves to be resurgent in $1/x$
(we shall explain what this means).

 


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Dernières modifications / Last modifications :  20 Février 2008