Finite Measures of Maximal Entropy for an Open Set of Partially Hyperbolic Diffeomorphisms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929337432801280 |
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| author | Mongez, Juan Carlos Pacifico, Maria Jose |
| author_facet | Mongez, Juan Carlos Pacifico, Maria Jose |
| contents | We consider partially hyperbolic diffeomorphisms $f$ with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of maximal entropy. Moreover, any $C^{1+}$ diffeomorphism near $f$ in the $C^1$ topology possesses at most the same number of ergodic measures of maximal entropy. Our contribution is in extending the findings in [4] to arbitrary dimensions. We believe our technique, essentially distinct from the one in that paper, is robust and may find applications in further contexts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02776 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite Measures of Maximal Entropy for an Open Set of Partially Hyperbolic Diffeomorphisms Mongez, Juan Carlos Pacifico, Maria Jose Dynamical Systems We consider partially hyperbolic diffeomorphisms $f$ with a one-dimensional central direction such that the unstable entropy exceeds the stable entropy. Our main result proves that such maps have a finite number of ergodic measures of maximal entropy. Moreover, any $C^{1+}$ diffeomorphism near $f$ in the $C^1$ topology possesses at most the same number of ergodic measures of maximal entropy. Our contribution is in extending the findings in [4] to arbitrary dimensions. We believe our technique, essentially distinct from the one in that paper, is robust and may find applications in further contexts. |
| title | Finite Measures of Maximal Entropy for an Open Set of Partially Hyperbolic Diffeomorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2401.02776 |