Global rigidity for some partially hyperbolic abelian actions with 1-dimensional center
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912057004130304 |
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| author | Sandfeldt, Sven |
| author_facet | Sandfeldt, Sven |
| contents | We obtain a global rigidity result for abelian partially hyperbolic higher rank actions on certain $2-$step nilmanifolds $X_Γ$. We show that, under certain natural assumptions, all such actions are $C^{\infty}-$conjugated to an affine model. As a consequence, we obtain a centralizer rigidity result, classifying all possible centralizers for any $C^{1}-$small perturbation of an irreducible, affine partially hyperbolic map on $X_Γ$. Along the way, we also prove two results of independent interest. We describe fibered partially hyperbolic diffeomorphisms on $X_Γ$ and we show that topological conjugacies between partially hyperbolic actions and higher rank affine actions are $C^{\infty}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00654 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global rigidity for some partially hyperbolic abelian actions with 1-dimensional center Sandfeldt, Sven Dynamical Systems 37C85, 37D30, 37C15, 53C24 We obtain a global rigidity result for abelian partially hyperbolic higher rank actions on certain $2-$step nilmanifolds $X_Γ$. We show that, under certain natural assumptions, all such actions are $C^{\infty}-$conjugated to an affine model. As a consequence, we obtain a centralizer rigidity result, classifying all possible centralizers for any $C^{1}-$small perturbation of an irreducible, affine partially hyperbolic map on $X_Γ$. Along the way, we also prove two results of independent interest. We describe fibered partially hyperbolic diffeomorphisms on $X_Γ$ and we show that topological conjugacies between partially hyperbolic actions and higher rank affine actions are $C^{\infty}$. |
| title | Global rigidity for some partially hyperbolic abelian actions with 1-dimensional center |
| topic | Dynamical Systems 37C85, 37D30, 37C15, 53C24 |
| url | https://arxiv.org/abs/2401.00654 |