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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.01321 |
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| _version_ | 1866916515813523456 |
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| author | Saghin, Radu |
| author_facet | Saghin, Radu |
| contents | We prove that for $C^{1+θ}$, $θ$-bunched, dynamically coherent partially hyperbolic diffeomorphisms, the stable and unstable holonomies between center leaves are $C^1$ and the derivative depends continuously on the points and on the map. Also for $C^{1+θ}$, $θ$-bunched partially hyperbolic diffeomorphism, the derivative cocycle restricted to the center bundle has invariant continuous holonomies which depend continuously on the map. This generalizes previous results by Pugh-Shub-Wilkinson, Burns-Wilkinson, Brown, Obata, Avila-Santamaria-Viana, Marin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01321 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On invariant holonomies between centers Saghin, Radu Dynamical Systems We prove that for $C^{1+θ}$, $θ$-bunched, dynamically coherent partially hyperbolic diffeomorphisms, the stable and unstable holonomies between center leaves are $C^1$ and the derivative depends continuously on the points and on the map. Also for $C^{1+θ}$, $θ$-bunched partially hyperbolic diffeomorphism, the derivative cocycle restricted to the center bundle has invariant continuous holonomies which depend continuously on the map. This generalizes previous results by Pugh-Shub-Wilkinson, Burns-Wilkinson, Brown, Obata, Avila-Santamaria-Viana, Marin. |
| title | On invariant holonomies between centers |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2307.01321 |