Ergodic measures of intermediate entropies for $\mathbb{Z}^{d}$-action
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914582831824896 |
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| author | Liu, Yage Chen, Ercai Zhou, Xiaoyao |
| author_facet | Liu, Yage Chen, Ercai Zhou, Xiaoyao |
| 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_21048 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ergodic measures of intermediate entropies for $\mathbb{Z}^{d}$-action Liu, Yage Chen, Ercai Zhou, Xiaoyao Dynamical Systems 37A35, 37B65 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. |
| title | Ergodic measures of intermediate entropies for $\mathbb{Z}^{d}$-action |
| topic | Dynamical Systems 37A35, 37B65 |
| url | https://arxiv.org/abs/2605.21048 |