5 problems

Let $G$ be the synchronisation diffeomorphism of the torus considered in the paper, and let $S$ and $R$ be the open basins of attraction of its corresponding asymptotically stable…

The Morse-Smale directional-flow conjecture. There is an open dense subset $U$ of $\mathbb{S}^{1}$ such that the directional flow of $X$ along any direction of $U$ is Morse-Smale.

Let $M$ be a Riemannian manifold with metric $g$, let $f$ be the function defining the virtually small spectral package, and let $a^q(M,g,f)(t)$ be the associated degree-$q$ analyt…

Morse–Smale hypothesis conjecture. The statement remains true without the hypothesis that $-\operatorname{grad}_g f$ is Morse–Smale. This would extend the theorem from Morse–Smale…

Arbitrary-regularity approximation conjecture. In any $C^r$ neighborhood of $X$, there exists a vector field that coincides with $X$ in a neighborhood of $X$ and satisfies…