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