Generic entropy flexibility conjecture for diffeomorphisms and flows

Entropy flexibility is the property that, for each admissible entropy level, there is an invariant compact set whose restricted system has that entropy. A property is $C^1$-generic when it holds on a residual set of systems. Generic entropy flexibility conjecture. Entropy flexibility holds $C^1$-generically for diffeomorphisms on a compact Riemannian manifold with dimension greater than one, and for flows on a compact Riemannian manifold with dimension greater than two. The source presents this as a question about whether entropy-flexible systems are large or negligible, following examples showing that an entropy-flexibility analogue of Katok's conjecture fails for both discrete-time and continuous-time systems. Its resolution is not indicated in the supplied text.