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Séminaire Géométrie et théorie des modèles

Horaires : Le vendredi 10 mars 2017, 14h15

Lieu : ENS, salle W

Quasianalytic Ilyashenko algebras

Patrick Speissegger (Konstanz/McMaster)

In 1923, Dulac published a proof of the claim that every real analytic vector field on the plane has only finitely many limit cycles (now known as Dulac's Problem). In the mid-1990s, Ilyashenko completed Dulac's proof; his completion rests on the construction of a quasianalytic class of functions. Unfortunately, this class has very few known closure properties. For various reasons I will explain, we are interested in constructing a larger quasianalytic class that is also a Hardy field. This can be achieved using Ilyashenko's idea of superexact asymptotic expansion. (Joint work with Zeinab Galal and Tobias Kaiser)

 

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