3 problems

Cohomology-free vector field conjecture. Any cohomology free vector field is smoothly conjugated to a Diophantine vector field on a torus.

For a perturbed family of interval exchange maps, persistence of invariant curves leads formally, as $\varepsilon\to0$, to a cohomological equation over the limiting interval excha…

For a smooth dynamical system, the scalar cohomological equation is the equation obtained by taking a smooth observable and a smooth coboundary; a system is $C^\infty$-effective, o…