Generic results in Denjoy-Carleman classes

Denjoy-Carleman classes are spaces of smooth functions which satisfy growth conditions on their derivatives. We distinguish the class of ultradi fferentiable functions of Roumieu type and the class of ultradi fferentiable functions of Beurling typ. Endowed with its natural topology, the Beurling class is a Fr échet space.
In the poster, we give a condition to have the strict inclusion of a Roumieu class into aBeurling class. We obtain then generic results about the set of functions of a Beurling class which are nowhere in a Roumieu class. Those generic results are obtained from three di fferent points of view: using the Baire category theorem, the notion of prevalence and the notion of lineability. We also study the particular case of Gevrey classes.