5 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 volume-preserving partially hyperbolic systems, meaning systems preserving a volume and admitting a partially hyperbolic invariant splitting. Generic exponential mixing co…

A vector field $X$ is called multisingular partially hyperbolic if its chain-recurrence set can be split into finitely many compact invariant sets, each admitting a multisingular p…

Plaque expansivity conjecture. Any partially hyperbolic, dynamically coherent diffeomorphism is plaque expansive.

Let $L$ be the hyperbolic automorphism under consideration, and let $f$ be homotopic to $L$ and partially hyperbolic in the strongest sense described by the source. Denote the rate…