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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.02397 |
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| _version_ | 1866929449605267456 |
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| author | Dong, Changguang Qiao, Qiujie |
| author_facet | Dong, Changguang Qiao, Qiujie |
| contents | In this article we study $r$-neutralized local entropy and derive some entropy formulas. For an ergodic hyperbolic measure of a smooth system, we show that the $r$-neutralized local entropy equals the Brin-Katok local entropy plus $r$ times the pointwise dimension of the measure. We further establish the existence of ergodic measures that maximize the $r$-neutralized entropy for certain hyperbolic systems. Moreover, we construct a uniformly hyperbolic system, for which such measures are not unique. Finally, we present some rigidity results related to these ergodic measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02397 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $r$-Neutralized Entropy: Entropy Formula and Existence of Measures Attaining the Supremum Dong, Changguang Qiao, Qiujie Dynamical Systems In this article we study $r$-neutralized local entropy and derive some entropy formulas. For an ergodic hyperbolic measure of a smooth system, we show that the $r$-neutralized local entropy equals the Brin-Katok local entropy plus $r$ times the pointwise dimension of the measure. We further establish the existence of ergodic measures that maximize the $r$-neutralized entropy for certain hyperbolic systems. Moreover, we construct a uniformly hyperbolic system, for which such measures are not unique. Finally, we present some rigidity results related to these ergodic measures. |
| title | On $r$-Neutralized Entropy: Entropy Formula and Existence of Measures Attaining the Supremum |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2408.02397 |