8 problems

Let $M$ be a compact $3$-manifold, and let ${\cal P}{\cal H}(M)$ be the $C^1$-open set of partially hyperbolic diffeomorphisms of $M$ admitting a dominated splitting … where all th…

Consider the space of diffeomorphisms with its $C^1$ topology. A global structural property and a robust local structure that obstructs it are assigned according to the particular…

Let $M$ be a closed differentiable manifold, and let $f\colon M\to M$ be a $C^1$-generic diffeomorphism. Denote by $\Omega(f)$ the non-wandering set of $f$. Arbieto–Bonatti–Diaz co…

Let $\Lambda$ be an aperiodic class for a $C^1$-generic diffeomorphism $f$, and let … be a dominated splitting such that $E^s$ and $E^u$ are respectively the maximal uniformly cont…

Let $M$ be a compact manifold and let $\operatorname{Diff}^1(M)$ be the space of $C^1$ diffeomorphisms. A diffeomorphism is hyperbolic if its nonwandering dynamics has a hyperbolic…

Abdenur–Bonatti–Díaz conjecture. $C^1$-generic transitive diffeomorphisms whose non-wandering set has a non-empty interior are globally transitive.

Let $M$ be a compact manifold, let ${\rm Diff}^r(M)$ be the space of $C^r$ diffeomorphisms of $M$, and call a point generic when it belongs to the full-measure generic set under co…

Let $M$ be a compact connected boundaryless manifold of dimension $d$, and let $\operatorname{Diff}^{1}(M)$ be the space of diffeomorphisms of $M$ with the $C^1$ topology. A homocl…