4 problems

Crovisier's conjecture. The bundle $E^c$ has dimension at least two and admits no non-trivial dominated splitting.

No-splitting conjecture. The class $\Lambda$ admits no non-trivial dominated splitting.

Contracted-bundle conjecture. The bundle $E$ is contracted.

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…