GT ADG-Systèmes Dynamiques
On the dynamics of vector fields having univalued solutionsLaura Rosales Ortiz (Université de Porto)
Tuesday 13 May 2025 14:00 - Orléans institut Denis Poisson - Salle de séminaire
Résumé :
The Painlevé test --a tool frequently used by physicists-- offers a
surprising way to guess if a system is integrable (i.e. has "tame" global
dynamics) just by looking at how its solutions behave near the
singularities. However, its success remains largely mysterious. In this
talk, we will look at a related notion: semicomplete vector fields, which
are vector fields possessing only univalued solutions. We will show how
certain local conditions around the singularities "constrains" the
complexity of the global dynamics of the foliation they define. Although
what should be considered as a "tame" dynamics is a slightly vague notion,
in this talk we will focus on its relation with the nature of the leaves
(hyperbolic, parabolic) and in the support of positive harmonic foliated
currents.
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