There exist transitive piecewise smooth vector fields on ${\mathbb{S}}^2$ but not robustly transitive

Rodrigo D Euzébio, Joaby S. Jucá, Régis Varão

It is well known that smooth (or continuous) vector fields cannot be topologically transitive on the sphere ${\S }^2$. Piecewise-smooth vector fields, on the other hand, may present no…