Katok's intermediate entropy property conjecture

Let $f$ be a $C^2$-diffeomorphism on a compact Riemannian manifold of dimension greater than one. The map $f$ has the intermediate entropy property when, for every number $0\leq c<h_{top}(f)$, there exists an ergodic measure $\mu_c$ of $f$ such that $h_{\mu_c}(f)=c$. Katok's conjecture. Every $C^2$-diffeomorphism on a compact Riemannian manifold with dimension greater than one has the intermediate entropy property. Katok proved this property for $C^{1+\alpha}$-diffeomorphisms on surfaces; the conjecture asks for the corresponding statement in all dimensions greater than one and remains unresolved here.