5 problems

Let $M$ be a closed Riemannian manifold, and let $f:M\to M$ be a partially hyperbolic diffeomorphism, meaning that $TM$ admits a $Df$-invariant splitting … where $E^s$ is uniformly…

Let $r\in[2,+\infty]$, and consider $C^{r}$ partially hyperbolic diffeomorphisms, whether volume preserving or not. A diffeomorphism is stably accessible if it has the accessibilit…

Let $f$ be a $C^{2}$ partially hyperbolic, volume-preserving diffeomorphism, and suppose that $f$ has the essential accessibility property, meaning that every measurable set satura…

Let $M$ be a manifold and let $f:M\to M$ be a partially hyperbolic diffeomorphism. For $x\in M$, the accessibility class $AC(x)$ is the set of points that can be joined to $x$ by a…

Accessibility-class regularity conjecture. Every accessibility class for $f$ is an injectively immersed, $C^r$ submanifold of $M$.