Crovisier's central-bundle conjecture for aperiodic classes

Let $f\in\operatorname{Diff}^1(M)$ be a $C^1$-generic diffeomorphism and let $\Lambda$ be an aperiodic class of $f$. Suppose that its dominated splitting is

$$E^s\oplus E^c\oplus E^u,$$

where $E^s$ and $E^u$ are respectively the maximal contracted and maximal expanded sub-bundles.

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

The conjecture is presented as a consequence of results known for aperiodic classes far from homoclinic bifurcations, together with the paper's theorem for Lyapunov stable classes. The source does not establish the full statement for arbitrary aperiodic classes.