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Bibliographic Details
Main Authors: Liu, Yage, Chen, Ercai, Zhou, Xiaoyao
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.21048
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Table of Contents:
  • 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.