Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913223945486336 |
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| author | Chen, Qinbo Damjanović, Danijela |
| author_facet | Chen, Qinbo Damjanović, Danijela |
| contents | This paper studies local rigidity for some isometric toral extensions of partially hyperbolic $\mathbb{Z}^k$ ($k\geqslant 2$) actions on the torus. We prove a $C^\infty$ local rigidity result for such actions, provided that the smooth perturbations of the actions satisfy the intersection property. We also give a local rigidity result within a class of volume preserving actions. Our method mainly uses a generalization of the KAM iterative scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_05091 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus Chen, Qinbo Damjanović, Danijela Dynamical Systems 37C15, 37C85, 37D30 This paper studies local rigidity for some isometric toral extensions of partially hyperbolic $\mathbb{Z}^k$ ($k\geqslant 2$) actions on the torus. We prove a $C^\infty$ local rigidity result for such actions, provided that the smooth perturbations of the actions satisfy the intersection property. We also give a local rigidity result within a class of volume preserving actions. Our method mainly uses a generalization of the KAM iterative scheme. |
| title | Rigidity properties for some isometric extensions of partially hyperbolic actions on the torus |
| topic | Dynamical Systems 37C15, 37C85, 37D30 |
| url | https://arxiv.org/abs/2202.05091 |