4 problems

Let $f$ be a partially hyperbolic diffeomorphism on a 3-manifold, with invariant splitting $TM=E^s\oplus E^c\oplus E^u$. Write $E^{cu}=E^c\oplus E^u$ and $E^{sc}=E^s\oplus E^c$. Th…

Unique-obstruction conjecture. The existence of such attracting or repelling $2$-tori is the unique obstruction to dynamical coherence.

Let $M^3$ be a 3-dimensional manifold and let $f:M^3\rightarrow M^3$ be a partially hyperbolic diffeomorphism. A $cu$-torus is a 2-torus tangent to the center-unstable bundle…

Consider orientable 3-manifolds supporting partially hyperbolic dynamics. Hertz–Hertz–Ures weak dynamical coherence conjecture. The only orientable 3-manifolds supporting non-dynam…