arXiv subjects
Publications and source records attributed to Yage Liu.
In this paper, we investigate a broad class of systems for which Katok's intermediate entropy conjecture holds. In particular, we show that a dynamical system with an amenable group action satisfies Katok's intermediate entropy conjecture provided that it has the specification property and is asymptotically entropy expansive.
For dynamical systems satisfying the approximate $\mathbb{Z}^{d}$ or $\mathbb{Z}_+^{d}$-product property and asymptotically entropy expansiveness, we establish a precise description of the structure of their space of invariant measures. In particular, we prove that the set of ergodic measures with any given intermediate entropy is generic in certain natural subspaces. As a consequence, this result confirms Katok's conjecture on the existence of ergodic measures with arbitrary intermediate entropy for such systems.