**abstract:**
An unfolding of a tangent to the identity diffeomorphism has an infinitesimal generator.
It is possible to embed the diffeomorphism in
the flow of Lavaurs vector fields by using auxiliary real flows of holomorphic vector fields. The Lavaurs vector fields are the natural candidates to be the sums of the infinitesimal generator in sectorial
domains. We explain why it is necessary to consider
more general transverse flows in order to prove the
multi-summability of the infinitesimal generator in the parameter variable. We give some applications
to the analytic classification of unfoldings.

Wed 14 Oct, 11:40 - 12:40, Aula Dini

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